The last time I was in France 10 euro might have been enough for a half dozen croissants or a bag of gougère. You're going to be biking and will need plenty of calories every day....good, full of good stuff kind of calories (ie. not bangers and mash). Might want to consider upping the food budget.
Tent - if you want to keep it really light go this direction:
http://www.thenorthface.com/catalog/...010-_-Deeplink
Train - There are trains that can easily accommodate you (same general idea as in the UK). Go here for all info:
http://www.sncf.co.uk/ Similar to the UK you can just buy your ticket at the station.
Panaracer Mach SS - these will not do, way to much tread. Go this direction:
http://www.biketiresdirect.com/produ...t-tire-26-inch
If the train will not accommodate a bike consider bus service.
Sounds like a fun trip. Have fun!