Dining with a view and best restaurant suggestions

Are you limited to the 7th and the 8th? If so, read no further because all of my responses are located in the double digit arrondissements.
Le Perchoir http://leperchoir.tv/
Brasserie Barbès https://www.brasseriebarbes.com/
Terass” Hotel Restaurant https://www.terrass-hotel.com/en/restaurant-and-bar

One of my favorite places for a view in Paris was O' Paris at 1 rue des Envierges in the 20th -- not a rooftop but a sidewalk cafe with great views across Paris. It closed and a new place is there called Moncoeur that I have not tried yet because I am still mourning the loss of O'Paris.

Les Ombres at the Branly Museum has a view of the Eiffel Tower, looking up through the glass atrium. Le Ciel de Paris at the top of the Montparnasse Tower has a fantastic view, including the Eiffel Tower and as far out as La Defence. Not sure at what point you would consider you are "breaking the bank." I consider both of these a bit of a splurge, but not excessively expensive. You can check their menus online.

I assume you mean Paris. Let me know if you're referring to the 7th or 8th arrondissements in Lyon.

Also -- keep in mind that Paris doesn't really have its own "local" cuisine or wine. Rather, restaurants in Paris generally serve food and wine derived from the regional cuisine of various areas of France, as well (of course) as international cuisine; commonly tweaked so as to not alarm the refined French palate (in practical terms, that usually means made sweeter and milder with respect to capsicum).

These museums also have nice rooftop views. I have not dined there.

• Institut du Monde Arabe: https://www.imarabe.org/en/practical-information/restaurants-and-cafe and http://www.noura.com/
• Centre Pompidou: https://restaurantgeorgesparis.com/en/