You can walk into any cafe and get a serviceable croque madame or messieur - or an omelet or a nice big salad. There's not much anyplace can do to damage any of those.

You really should not "aim" at some place specific in my opinion. There will be "something" for you to pick up something or to go into.
If your tour is so tightly bonded at a lunch time, you need to plan ahead by getting some bread, etc. as you have already suggested to yourself.

The bread will be stale by the next day, if not before.

I would not worry about where to have lunch. Since you're on a tour, your guide will be able to suggest the best places to eat.

There are several cafés on the square in front of Trinité, one even has a big counter with sandwiches, etc. to take away. Just up rue Blanche is Le Brigadier, wihch has a good reputation.

Your biggest danger around ND is that many of the places right around are tourist traps. Cross over to Ile St Louis to get away from the tourist traps and enjoy the many restaurants that line the main street. The island is very charming and I bet you will get better food.

Trust me, you won't go hungry in Paris.

The restos on the Ile St-Louis are no less touristy. However, on either island, you will have no trouble finding a light lunch.

Thank you everyone for great response and ideas. I knew the Fodorites wouldn't let me down. @Louie, thanks for a name - instead of wondering about we can head straight to the cafe. @denisea, sounds like a good idea. @toupary I had to laugh at the comment of not going hungry in Paris.

I agree that near ND, Ile de la Cité, and also just across the river on the left bank at St. Michel are all touristy - though that doesn't mean so much bad food as bad prices!

As mentioned up-thread, you can get good basics at any café or brasserie. On Ile de la Cité, if you walk closer to La Conciergerie, the cafés on Blvd du Palais, while still basic, serve lunch catering more to the nearby government workers than to tourists.

If you want to embrace the scene and don't mind a touristy place, IMO the best option is the Café Le Depart on the Place St. Michel on the corner near the Seine. I have periodically enjoyed a café or pression there for decades - the people-watching is great.

The streets immediately surrounding Place St. Michel are home to many Lebanese and other Middle-Eastern take-away shops, with their windows filled with pastries dripping with honey. Try wandering up Rue St. André des Arts towards Odéon, which also has its share of crêperies, frites Belges, etc.

And of course I'd be remiss if I didn't remind you to save time for a glace at Berthillon on Ile St. Louis!