A collection of tips from travellers at Concierge.com included one that appealed to me: make your first stop a food market.
Big markets like the Boqueria in Barcelona can be a real pleasure to peruse. In smaller French towns it's worth noting what day the local market is; you'll get brilliant fast food (though it may include andouillettes, or 'shit sack sausages' for those who don't like them). Even rather boring places like Boulogne, where Speedferries arrive and most cars head straight out of town to the motorway, can be transformed in market hours, when fishermen unload their catches at the quay.
But I'd say, don't overlook the appeal of supermarkets. Spend some time in a Champion or Leclerc for instance, and you'll get a feeling for the real differences between the French and the English attitudes to food. No baked beans, certainly not an entire side of one aisle given over to different brands of tinned beans and spaghetti. Fresh fish including a lot of spiny, odd things you won't have seen before, and, usually, oysters and fresh mussels. An absolutely massive range of cheese, usually including at least one local cheese.
And labels on all the fruit and veg (and meat) telling you where it's come from - if it's French, even telling you the département where it originated.
Plus, a choice of beef according to the breed of animal.
So always head for a food market, or a supermarket, or just a corner shop, and find out what people eat... and you will find out, without really trying, about the local culture.