Try at least one of their bistros. I felt they provided the local experience I was looking for in Paris. Bohemian Quarter? Are you referring to Montmartre? I'd recommend Le Bistrot du Maquis. For newcomers, they even pour wine for you and provide a tour while walking you through their menu.
For nearby Sainte-Chapelle, try Le Petit Pontoise. This bistro gives me a nostalgic feeling of Paris.
There are other French bistros in Paris. You can check them out. https://happinessontheway.com/french-bistros-in-paris
You can also walk around Rue Cler and find several restaurants, cafes, and stalls. What I love about it is seeing locals go about their everyday shopping for fresh ingredients.
Paris is also known for its Michelin-starred restaurants. There are several scattered around the city. What even surprised me is that you can find affordable options for around $50 if you come for their lunch menu instead of dinner.