I've registered one UK bike two years ago and have to register another fairly soon.
The first was registered using the old system and took no more than 2 days of visiting different local offices. Unfortunately the system has changed to an online one and it was (and might still be) having serious delays of up to 3 months or more to get your logbook (Carte Gris). I think this has improved a lot now, however.
Please research and check the following, but just to give you an idea.... You can't register any bike here over 106bhp unless it was fitted with ABS as standard. You will need a Certificate of Conformity which is available from the UK importer, don't pay someone else (ie Eurococ quoted earlier) to do this unless you don't fancy sending a couple of emails and taking some pics (it was that easy with KTM). You will also need a receipt for the bikes showing that VAT was paid (if it was new when you purchased it) or just a hand written one if the bike was bought secondhand. You will also need a utility bill showing your French address. I can't recall if you also need a Certificate de Attestation (proving that you are resident in France and obtainable from your Mayor).
To access the online system you need to register first, which involves your postie verifying your ID(!). Then you can apply online sending scans of the above documents plus your V5. A really good thing to do is make sure every document you provide has the same name and address on, it can have a UK and a French address, but only one of each.
There is a FB group called 'REGISTERING RHD VEHICLES IN FRANCE' that gives excellent up to date advice, including a guide or two.
It might sound daunting but it really is just a paper exercise and as long as you give them everything they ask for, with the right address and name on it, it's fine. The people that have trouble are the ones who don't give them what they ask for!
I think I paid about 100 euros all in for a 04 KTM Adventure. 2nd hand bikes are very expensive here and from experience not well looked after, or presented at a dealer. So unless you want to buy a new bike when you get here, bring your bikes as long as you are 100% that they can be registered here. I thought I'd checked everything before we came here, but I still ended up with four bikes I can't legally ride here as well as being caught when they upped the charges for registering cars here. So if you can get a CoC and the bikes have ABS, I would say bring them, but only if you're good with paperwork. It would cost you a lot more to replace them, like for like, in France.
If you get stuck with anything or have any other questions that I might be able to help with, let me know. I'm hoping to register my 350 EXC in the next 3 or 4 weeks, so should be able to give better info on the new system.
Best advice I can give is the same as someone gave us when we got here, 'don't try to beat The System, because you won't and Keep it Simple, Stupid. The French LOVE admin!