I went in 2005, but my trip was significantly different. I found a B&B in Rennes les Chateau, flew into Toulouse with my bike in a bike hard case as one of my checked pieces of luggage, and got picked up by the owner of the B&B.
There was a lot of logistics and planning involved to get my bike and spare parts over there, but it doesnt sound like you'll be doing that. The Tour came by one day on its way to a mountaintop finish in the Pyrenees, so I planned to ride down to the top of the Port de Pailheres, and did. Quite honestly, one of the most amazing days I've ever had. Certainly on a bike. Rode all over that area for the next three weeks. I had plans to also meet the Tour another day but blew it off, as it was a peloton zooming by on a flattish area (I would not have been at the finish line) and I was having simply too much fun riding and exploring. Being on a mountain for the Tour... astonishing.
Some random advice that would still be relevant:
Get some Michelin maps of the area you will be in. They are accurate and detailed.
I didnt know any French over there and they dont speak a lot of English in certain parts of France, but brush up at least on a few greetings and how to ask a few questions etc. How to ask for water is a really good one. You'll need it. It was amazingly hot over there. I got by mostly with a nice greeting, a smile, and pointing and gesturing at things. They were so nice over there.
Book your points of stay very, very early. This part of it takes a fair amount of planning, especially if you're looking to meet up with the Tour at a few locations. Sounds like you'll be camping, so maybe not as much an issue, but that will have its own things to consider and someone who has done that will need to advise you. You might want to book a place or two to stay to freshen up in between camping. You'll still need to plan carefully where you are one day, where you need to get to the next. Get a Michelin Green Guide while you are at it, for the area(s) you will be in. They listed transportation and camping options. You may wish to call some of the phone numbers ahead to ask questions.
Plan the water thing. I had bottles on my bike and a Hydra backpack too. Full. I still had to stop and get a water refill at a gas station at the foot of the climb and then again on the way up the mountain and then again on the way home. Was a 120+ mile round trip and it was ~100 degrees that day. I was cycling, it was the south of France, and it was unusually hot even for there, so it may differ for you.
The sun beats down on you something wicked if the sky is clear. Bring a hat of some sort. Dont forget the sun block.
Bring a camera of course. Such a memorable trip. I'd do it again in a heartbeat. Planning another maybe in two years or so. Have fun!
