Two of our favorites -- and if you have never been to Paris you really should go for some 'fine dining' are Coretta on the edge of MLK park near the Pont Cardinet stop of the 14 metro
https://www.restaurantcoretta.com
and L'Initial in the 5th near the river which has a lovely tasting menu with choice for the meat course. We have eaten there several times and never been disappointed.
https://restaurant-linitial.fr. The dinner tasting menu is 68 Euro without wine and you can either get a bottle of wine or wine pairings -- we don't drink a lot and usually have a glass of Champagne and then water. The cost of wine pairing would not be worth it to us, but if you like wine with your meal then it is one way to have a variety matched to the menu.
At any restaurant you can get a free carafe of local water usually chilled and always good. At a splurge we usually get a bottle of bubbly bottled water -- but this is an expense you can easily forego.
Coretta has modern decor -- you are sort of in a tree house over the park and l'Initial has a plain room/excellent service. There are a number of places with fancy rooms. Train Bleu -- gorgeous room, so so food; Bofinger good copious alsacian food and spectacular room (if you go there ask for the main room when you reserve). Les Ombres has a good view of the Eiffel tower through it's glass roof; we only ate there once long ago and the food was so so but they have probably had 3 chefs since then.
Always reserve for a restaurant you want to eat at -- you will always find something walking in but they are likely to be restaurants where there is a good reason they have last minute availability. for any of these restaurants I would reserve as soon as you know your dates. All of these are moderately priced. Not inexpensive but nowhere near 'ultra fine dining' costs in Paris.