Restaurant near Eiffel Tower with a-la-carte menu

The Michelin Guide has a good list: use google translate as needed. I do not share their enthousiasm for Monsieur Bleu.
Many fancy places have set menus, alas. None of the ones I have in mind (Etude, Les Ombres) do à la carte, but maybe some of the recommendations above do?

La Fontaine de Mars on Rue Saint-Dominique might suit but fair warning, there are those who say it is resting on its laurels. Or how about Le Petit Cler on Rue Cler. Are you looking for a restaurant with a view of the Tower or just near it?

Do any of these interest you? They are much less than your price point so might not be what you have in mind.

La Terrasse du 7eme - right by the Ecole Militaire Metro stop

https://www.laterrassedu7.com/en

Further down Avenue de la Motte Picquet....

Auberge Bressane
https://www.auberge-bressane.com/

Cafe Max Invalides
https://www.cafemax.fr/fr
Some history on Cafe Max which is located between Les Invalides and the Ecole Militaire where German troops were stationed during WWII.
https://www.sortiraparis.com/en/where-to-eat-in-paris/restaurant/articles/282172-cafe-max-generous-french-cuisine-in-this-resistance-stronghold

I would avoid restaurants at the intersection of Avenue de la Bourdonnais/Avenue Rapp/Rue Sainte-Dominique. I see people complaining on FB sites that they've gotten ripped off with high prices not shown on the menus and getting asked for tips by servers. On down Rue Sainte-Dominique is fine which is where one of the above restaurants is located, just not at that intersection.

I second Auberge Bressane. I was going to mention it above but I thought it might be too far away from the Eiffel Tower. Also, take a look at Le P’tit Troquet and L’Ami Jean.

JHK, I wondered as well if those locations would be convenient. Having now checked, it looks like from a prior thread that the OP is staying just west/SW of the Eiffel Tower between the Bir-Hakeim and La Motte-Picquet Grenelle Metro stops. It's a mile or so to walk or they can hop on the Metro for 1 stop (from La Motte-P) if tired.

I look at Auberge Bressane every time I go to Paris and have not taken the leap to go there. It'll have to be a non-vegan night for me because the Grand Marnier Souffle sounds wonderful, lol!

Thank you for the suggestions. I will check all of them online if possible and prebook one. The reason I want it close to the Eiffel tower because I booked a visit there in the late afternoon and thinking to walk to a nice restaurant nearby after the tour. Taking a short taxi trip not a problem either.

I’ll echo the recs for Auberge Bressane. Honest food at reasonable prices. And yes, the GM soufflé is wonderful. And do make a reservation, at least two days ahead, especially if you want to dine there in a weekend.

I find the walk from the Eiffel Tower to the area of the Ecole Militaire Metro stop to be easy and enjoyable. Not sure what the Champ de Mars will look like when you are there and if it will be a pleasant walk or still obstructed with Olympic stuff but if available I’d put the ET at my back and walk toward the Ecole Militaire (where Napoleon was a cadet) at the other end of the green space. Take a left when you reach the end of the garden and walk to any of the 3 on Av de la Motte-Picquet if they are of interest.

If you want a taxi home, there is a taxi rank at the La Tour Mauberg metro stop just around the corner from Auberge Bressane.

What a fun birthday!

Le P'tit Troquet is lovely. The menu is a-la-carte. I went because I believe it was recommended by David Lebovitz. It is only a 10-minute walk from the ET. I second La Terrasse du 7ᵉ.

I am reopening this topic with a little additional question - any of those restaurant or maybe some else offering a live music on the weekends?

That would be unusual in Paris. I didn't say impossible, but space is at a premium in the city, and most restaurants are too small to have any space for musicians.