Mid June - Aug 1, less than 1000 miles. I had lots of rain (the worst summer in 130 years, I'm told) and lots of sights to see, which slowed me down; I stayed in some places (Blois, Angers, Honfleur, Rouen) as long as 3 or 4 days.
I flew with my bike to Paris, where my brother lives, attended his 50th birthday bash on a barge on the Seine, then took the R.E.R. to Versailles to start the tour; then Chartres, Chateaudun, the Loire Valley (beautiful chateaux, but nearly constant rain throughout beautiful countryside that normally has beautiful weather that time of year) to Angers, north through eastern Brittany (when the weather started to clear) to Dinan and St. Malo, east to Mont St. Michel (amazing fantasy abbey rising out of the mists), around the bay to Granville, across the Cotentin peninsula to the D-day beaches and Bayeux (Battle of Hastings history and WWII history intertwined), continuing east through Normandy (wet weather again) to Honfleur (where the weather cleared again; home of impressionism and my favorite), continuing east to Jumieges (the only ruin that gets Michelin's "must see" 3 stars) and along and across the Seine (3 ferry crossings) to Rouen (a wonderful city of architecture and Joan of Arc, whose story moved me deeply), further along the Seine to les Andelys (site of the ruins of Richard the Lionhearted's Chateau Gaillard, built in 1196; a fairly "typical" sight for this tour!) and then east through Ile-de-France to Chantilly (about 50 miles north of Paris), took the R.E.R. to Paris on July 27 to watch the finish of the TdF (I got a blur of spinning wheels on film), returned via R.E.R. to Chantilly (had no place to stay in Paris until Aug 1), went on to Compiègne (site of the Armistice signing of WWI and Hitler's turning the tables on the French in WWII; nice town and large and beautiful surrounding forest), returned to Chantilly and took the R.E.R. back to Paris.
I speak minimal French. The most trouble I had was that I was isolated, traveling alone and with few people I could communicate with in any depth. It helped that I could call my brother every few days. As far as necessary communication, of course it took some effort, but I could get a room in a hotel, find out where things were, buy things in shops, check into campgrounds, and so on with a phrase book and jestures. The most essential phrases are "s'il vous plait", "bonjour, Madame/Monsieur!", "merci" and "pardon". If you can say those, you will magically discover that most of the French are very pleasant and helpful and that many of them speak "a leetle beet" of English; if, like many Americans, you just start speaking English or making demands, you will find that the French are rude and arrogant and none of them speak any English at all.
As I understand it that's not ok in France; there is no "free camping" on public grounds. On private land, I understand that many farmers will let you pitch a tent if you ask. But there is a campground in virtually every town, many of them are beautifully and/or conveniently located, and so that's what I did when I tented (but I also spent a fair amount of time in hotels, given that I can afford it, that I tend toward insomnia, that I had a lot of wet weather, and that I have a hedonistic streak).
I did see some people (no bikes) with a tent in some woods off a path near an ocean overlook; I suspect they were locals because it wasn't on a road from anywhere to anywhere. Other than that, I never saw anyone camping other than in campgrounds and backyards (which is quite popular.)
I didn't see very many touring cyclists during the rainy periods. I bumped into a couple (he was French, she was Minnesotan) at Chateau Chambord; I had been on the road 4 days, they for 2 weeks. We swapped experiences about weather and French drivers (they were very positive toward them, I was still rattled; I got more positive as I got more used to them). I bumped into a couple and their infant at a very cheap hotel near Chateau Chenonceaux when I came in from the pouring rain; he was British and she was Finnish. We swapped experiences about the weather. They were on a two week tour, and unfortunately were doomed to nothing but rain throughout the Loire, and with the baby on a seat on the back yet! Later I saw quite a few tourists on the roads, mostly heading the other way of course. I chatted with a with a family (Swedish, perhaps) of five while going up a steep hill near Trouville, had a long conversation with an American fellow at Mont St. Michel who was on a tour similar to mine but headed in the opposite direction (we were both using the Whitehill's France by Bike). Occasionally I saw a tandem or a trailer going around a corner in some town, or other cyclists pedaling away from a tourist office just as I'd come up. The campgrounds are the place to meet fellow riders, but I was usually tired and tend to be shy about walking up to people.
There were of course French women carrying groceries, kids, old men on weekend morning rides. At one point I was passed by two French men and a French woman in jerseys on an uphill, then I passed them on a downhill, then we played a bit of leapfrog until our routes diverged. They smiled and spoke to me but all I could reply was "Je ne parle pas français".
At some point in Brittany I crossed the route of the TdF, but I'm not sure where. And of course I saw hundreds of cyclists on the Champs-Elysees at the end of the Tour; casual riders, tourists, weird setups, all sorts of stuff.
No, see above. French nationals and more experienced tourists would be more reliable sources of information than I am.
Behave like a guest, educate yourself about the location before you get there and each place you go via tour books, the web, and visits to the local tourist office. Treat differences in culture and habits as an exciting learning experience and a source of diversity. Open yourself to a richness in history unlike anything you have experienced in the U.S. (if you are from the U.S.).
I recommmend Rick Steve's Europe Through the Back Door for general philosophy on how to behave and how to make the experience richer, except that I would slow way down from his whirlwind tours. If you only have a couple of weeks, explore some place in depth instead of rushing from place to place. Europe is not like the U.S. with vast stretches of wasteland that it makes sense to ride for 75-100 miles at a time.
One day in the Loire Valley I hit 4 chateaux in 30 miles and spent 1-2 hours at each. I had a severe case of bronchitis in Dinan, at the foot of the beautiful Rance Estuary, and spent 6 hours riding 15 miles up the estuary, stopping every 20 minutes or so for a photo op, a picnic, to bask in the sun, to take a hike along the tow path or in the woods above the estuary, to watch kids on paddle and sail boards, etc., until I reached the Breton beach resort of St. Malo, a lovely walled town on the English channel where Chateaubriand stood on the walls and dreamed of joining the fleet.
I checked into the hotel where I had called ahead for a room (the only time I did that), discovered that my room, which was nearly the cheapest in town, was also nearly perfect, put on my swimming trunks, walked around a corner from my perfectly situated hotel to one of the portals through the wall, and went out and laid on the beach among a bevy of topless French beauties to soak up the sun and let the bronchitis drift away.
In another case, my guidebook had me going 86 kilometers (54 miles) from Bayeux to Honfleur in a day. The weather was grey and drizzly on and off. I wanted badly to see Honfleur in the sunlight, as it had been captured by all those impressionists.
I took three days to get there, getting a chance to thoroughly explore the beach and casino resort towns of Cabourg (a haunt of Marcel Proust and home of the international bridge tournament), Deauville (home of the American Film Festival), and Trouville. During an hour here or there among the rain, I got to walk along a boardwalk in the evening with hundreds of Cabourgians braving the wild winds, roaring sea, and beautiful sunset, and I got some ice cream at the beach in Deauville where everyone was out under their colorful sun umbrellas, only to walk out of the ice cream shop to find a black cloud rolling in and scattering the bathers for the rest of the day. When I rode to Honfleur it was grey all morning; I pitched my tent at the grungy town campground that was only a 5 minute walk from the town center, walked into town, stopped in one of the hundreds of art shops there, and walked out to find the sun shining and the multicolored sails of the old pleasure boats reflected in the "vieux bassin", the old dock, a square body of still water surrounded by tall, narrow, beautiful half-timbered and stone buildings also reflected in the water. This glorious place and the beautiful and peaceful surrounding countryside was my welcoming home for the next three sunshine-filled days and warm evenings. Rick Steves suggests getting there late and leaving early the next morning; hurrumph! I might have done that if I had ridden there straight from Bayeux; I would have missed so much.
France, at least, is a beautiful combination of countryside, wildflowers, farms, hills, rivers, castles, churches, villages, ports, people, culture, and history. I think it is a mistake to simply ride through it rather than into it.