As a Frenchman who lived in the 6th arrondissement for many years and still goes there on a regular basis, may I make a few suggestions of nice bistros and restaurants that are open in August: But you check the info on their respective sites on the Internet.
Cafe Constant 139 Rue St Dominique and Les Cocottes , on the same sidewalk Rue Saint Dominique in the 7th.
(2 very good bistros)
Chantairelle 17 rue Laplace in the 5th ( very picturesque. very tasty cuisine from Auvergne)
Les Vignes du Pantheon 4 Rue des Fossés St Jaques in the 5th ( they might be closed in early August)
La Bastide Odeon 7 rue Corneille in the 6th ( provencal cuisine)
Le comptoir du Relais 9 carrefour de l'odeon 6th ( modern bistro)
Aux Charpentiers, 10 rue Mabillon 6th ( old traditional Bistro)
La fontaine de Mars 129 Rue Saint Dominique in the 5th (good cassoulet and duck)
Polidor 41 rue Monsieur le Prince in the 5th ( very simple bistro but charming)
La rotisserie d'en face 2 rue Christine in the 6th ( good and open late)
L'Ambassade d'Auvergne 22 rue du Grenier Saint Lazarre in the 3rd ( very goood traditional restaurant with fanatstic cuisne from Auvergne)
And of course 2 old but still good brasseries:
Le Balzar 49 rue des Ecoles in the 5th
La Coupole 102 Boulevard Montparnasse in the 14th but close to the 6th
You can find a few descriptions ( dated 2006) on my blog: French Virtual Cafe
Alain40