We will be in Paris in early May and are looking for recommendations for quaint restaurants in Left Bank and Marais.
That is very broad. What is "quaint" to you? Do you mean traditional food, traditional setting, both? Also, where in the left bank?
Specifying a bit more will get you better advice :-)
Welcome to the forum!
You may find something that is quaint near your hotel. Agree with Balso, a little more information would be great.
I, personally, love the falafel in the Marais. To me Mi-va-mi feels very quaint and the food is wonderful. It's right across from the more famous L'As du Fallafel but I like the food better at Mi-va-mi. This may not be YOUR idea of "quaint" though....
By your description (you do not mention capability of the kitchen), what you are looking for is le Coup Chou in the 5th arrondissement. Reserve early and get a table by the fireplace:
what did you think of Rick's recommendations? And Frommers? And Trip advisor? (hint, hint)
I can highly recommend https://www.yelp.com/biz/la-maison-du-jardin-paris