How to take a bike by train in France ?

Does anyone out there have the slightest idea how to take your bike on the train over to France ?
I would like to be able to take the Eurostar over to France and then take my bike with me on the train down to see a stage or two of the Tour de France.
It sounds simply, doesn't it ? But try as I might, I cannot get a definitive answer as to which trains allow bikes and under what conditions.

Let's start with Eurostar. They seem to say you can take a bike over to France as 'hand luggage' if you dismantle the bike and put it in a bike bag. However, their terms are littered with phrases like, 'if space is available'. They also state that bikes must go in luggage racks on the trains, which I know from experience are often full up with spotty students' ruck sacks, or posh skiers enormous bags.

Then when you get to France, the fog surrounding transporting bikes becomes totally impenetrable. I have looked at the SNCF web site which says that some trains do and some trains don't take bikes and some bikes will go with you on the train, whilst at other times they may go on separate trains and may even arrive at the same station as you - but not necessarily on the same day !

I have even tried going to 'Petit France'in the West End and asked the 'experts' in the SNCF offices, but they just look blankly at you and offer such helpful advice a 'just go over to France and see what train you can get on' !

About 15 years ago I did do just that - and it worked ! I got the ferry over to Calais and bought a ticket to La Rochelle. However, even then it took me 45minutes of school French to book the ticket only to discover that I changed in Paris overnight, but my bike went straight there - presumably on its own by magic

Surely there must be an easier way to arrange something like this ?.