Assuming your question is about bikes that aren't in a bag, you need to get on a TER local train (not a TGV). I've had a quick look at the timetables and the trains seem to be every couple of hours.
You can check train times (although not for June just yet) on
www.tgv-europe. Click on the tab marked '+détails' and look for the blue bike pictogram. I've uploaded a screenshot to give you an example of what to look for (the screenshot is from the main SNCF site so is in French - tgv-europe is in English).
And here's a link to some information on what to expect on the train:
http://www.fubicy.org/spip.php?article109
Fubicy is one of the French cyclists' organisation