Baguette and brie is useful food and you can just break a chunk off the brie, pull off a lump of bread and squish the brie inside the bread.
However, it might be worth keeping a knife and chopping board, napkins and plastic plates in the car (or picnic kit) if you want to be a bit more civilised about this - maybe that's how French travellers do it?
Eat French food and if your DCs can't do without Heinz beans or anything else that will be expensive there, take your own if you can.
If you have a slow cooker, you could take it with you to make a cassoulet type meal while you are out for the day with tinned or bottled beans, veg and sausages - eat with crusty bread.
Bottled water (big basic bottles not Evian etc) is probably pennies in the supermarkets so don't worry about buying that if the tap water doesn't agree with you.
Could you boost your budget a little by using the money you would have spent on food at home or is that already included in the £250? Also make your money go furthest by reading the moneysavingexpert article on travel money - there can be a 10% difference between the best and worst ways to exchange money.
Also, as it is quite late in the season, friends and family may already been on holiday and have euros left over - why not offer to buy them off them at the official bank exchange rate (currently 1.158 Euro to the pound - see www.xe.com/). You won't get any better than this and they may prefer to have UK money now, rather than having it hanging around for their next holiday bloody hell that exchange rate has dropped a lot bastard brexit