I was comparing travel times from Bayeux to Avignon with both web sites and raileurope seems 1 hour faster compared to the French system.
I think we are using the same trains.
Are these quote reliable?
I'll throw one more timetable site into the mix. The best site for most of Europe is the German Rail site, www.bahn.de. Click on the drop-down menu in the upper right-hand corner for English. After you get summary timetables for Bayeux-Avignon TGV, click on "Details for all" to see the connecting points.
The time difference is very likely because you may be going from Bayeux to Caen for the tgv to Paris for connections also via tgv to Avignon. There is also the route that takes you mostly via the mainline system via St Pierre des Corps (Tours), which is slower. The whole tgv system uses Paris as a hub just as the air travel system does.