France has a genuine reputation for welcoming dogs into restaurants and cafés, and it holds up better than most countries' version of this stereotype. There's no national law banning dogs from dining rooms — the decision is left to each restaurant owner, who generally doesn't have to justify saying no. What does exist is a hygiene rule, usually enforced through departmental sanitary regulations, that keeps animals out of food preparation, storage and sales areas — meaning the kitchen, not the dining room itself.
In practice, this means the overwhelming majority of French café and brasserie terraces welcome a well-behaved dog without a second thought, and a large share of indoor dining rooms do too, particularly in casual and mid-range restaurants. The exception tends to be more formal dining rooms, where it's genuinely worth asking first rather than assuming.
One group of dogs has a stronger legal footing than ordinary pets: guide and assistance dogs have a long-standing right of access to any place open to the public, restaurants included, dating back to a 1987 law and reinforced by France's 2005 disability rights legislation. Refusing entry to a recognised assistance dog is a separate offence from simply declining an ordinary pet, carrying its own fine.