Touring Europe (Tour de France) questions

Hi

I am posting on here about bicycle travel to France on American
airlines to see if anyone
recently has does this. I searched this group but all the postings I
can find are from 2003 or earlier.
I want to plan a trip to see the later stages of the Tour de France.
I
already have a plane ticket to
Orly airport and a Rail Europe anywhere/anytime France ticket. I know
American airlines charges $100 for bicycles. I still have a few
questions.
1. Does Rail Europe thru France allow bikes on the train without a
case or box?
2. Where do you store the case if it is a large plastic one? (I was
thinking about getting a nylon one so it is easier to store in a
locker at the airport or at the trail station where I arrive,)
3. Does the train going to London under the chunnel (eurostar) allow
bikes? (I'm planning on going to England after the Tour)
4. Does anyone have any experience spectating the Tour de France with
their bicycle as the main means of getting around? Then leaving by
train and air?
Thanks for any help .
Jeff
)