Early Dinner near Rodin Museum or Eiffel Tower

There is a tiny Italian deli, "Da Rocco", at the corner of rue de Grenelle and rue de Bourgogne very close to Musée Rodin. It is open non-stop, as long as they are not on vacation on 18 July. There are a few tables inside, or you can grab stuff to go.
Otherwise, for picnic supplies, there is a Carrefour City supermarket at Ecole Militaire, and several stores off rue Cler.
And the Rodin museum has a café on the grounds.

There are tons of Monoprix all over the city, their takeaway food is quite good. Or a small Carrefour. You can Google map for specific locations. You're also not too far from Bon Marche which has a huge supermarket/food court.

Thanks so much!!

a lot of the bars and cafes along Kleber Avenue are catering to the embassy/consulate workers in the neighborhood who are on different time zones.

for instance:
http://www.cafekleber.fr

Many of the restaurants along Rue Cler, Rue de Grenelle and Rue Sante-Dominique have continuous service. There are also several boulangeries on Rue de la Motte-Piquet and Rue Cler, Avenue Bosquet and Avenue Bourdonnaise for picnic stuff.

The restaurant next to the above mentioned Carrefour, La Terrasse du 7eme is service continu as well.

https://www.laterrassedu7.com/en/brewery/

Pam is right, there are many places in that area open all day. One of my favorites is Alfio, 43 rue de la Bourdonnais, very near the Eiffel Tower. Great pizza! Enjoy your time in Paris!

Fantastic! Thank you all! Looking at Google Maps and clicking on random restaurants to see open hours was getting a bit daunting!!

Honestly I think you can just walk from the Rodin and once you are on the other side of Les Invalides start looking to see what looks good to you!

FWIW, I was at the Rodin in early December and the cafe was not open. that may now be different.

Also a suggestion on the Rodin, start with the outside loop. You'll see actual statuary. When you go inside, after a while you'll find it's a bit repetitive, because they will show you all the preliminary sketches and and drawings and tests before making the actual work.

Also if you can't get to the museum or you run out of time, it turns out the Orsay has a bunch of his works as well.