TheFork users who ate in Annecy have said really good things about La Taqueria by Los Primos, Los Primos and Ailleurs qu´Ici. Maybe you should give them a try!
Some of the more popular Dog-Friendly restaurants where you can go with your family in Annecy according to TheFork users include:
La Taqueria by Los Primos, with a 8.7 rating
Los Primos, with a 8.8 rating
Flora, with a 8.3 rating