The few Italian places I tried (and also talked with people living longer in Boston) in North End are a waste of time. If you really have to eat at one in the North End I would pick Mamma Maria. Some other options for good Italian restaurants outside of North End are Coppa, SRV, Posto, Fat Hen, Giulia, La Morra - you should look at the different menus as all of them have different directions of the type of Italian dishes.
If you like Napolitanean style pizza I highly recommend Area Four (they have two places - Kendell Square and South Boston - try the one in SB as it has a bigger menu, especially the very good appetizers.)
When you asking for French, are you asking for “classical” French or French inspired restaurants ? I don’t think “classical” French is a strength of Boston but there are a few restaurants like Les Sablons, Ma Maison, La Volie (haven’t visit those).
Good new American, chef driven restaurant are plenty and you should check the locations and the menus to get some ideas - Sycamore, Alden & Harlow, Backroom at Moody’s, Townsman, Little Donkey, Waypoint, Commonwealth, Field & Vine, Cultivar to name a few.
Best bar so far in Boston for us is Backbar, other good options are Wink & Nod (hosts 6 months pop-up restaurants for their food), Eastern Standard, State Park, Blossom Bar, Brick & Mortar (but most restaurants tend to have excellent bar programs - often better what we had in San Diego or LA).