Our touring style has recently become a late lunch after breakfast, then a smaller snack in the evening. I have not paid much attention before to how late one can commonly arrive at typical small Paris resto for lunch. I'm guessing that 1:30 is generally fine, but is 2 PM pushing it a bit? I know this is a rather general question, but any experiences here would be welcome. Thanks.

We often eat at around 2. I think 2 is fine but 3 is probably too late, depending on the restaurant. You can check the websites of the restaurants. Many cafes stay open all afternoon.

As a general rule, cafes and brasseries serve straight through. Just make sure you order dishes that can't be reheated (don't order Poulet Roti in the midafternoon). Many bistros now try for multiple turns at lunch, like L'Ardoise etc. They might serve you up to 3 pm.

you'll find out, but if you literally mean restaurant as you say, you cannot arrive in the middle of the afternoon at a restaurant and be served, I wouldn't try 3. I think 2 pm is usually okay. Some close around 3 or 3:30 and reopen for dinner later. If you go to brasseries or cafes in the middle of the afternoon, they may not be able to serve you the full dinner menu or things like that.

What Christina said. You can get something to eat but you won't usually be able to get everything to eat as early as 2:30, as I have learned sadly.

In a café or brasserie, the service is generally non stop (also in the chain restaurants like Bistro Romain, Chez Clément, Léon de Bruxelles, Hippopotamus -- which even gives a 20% discount after 14:00 -- Buffalo Grill, Indiana).

You can forget "a typical small Paris resto" if you are late -- 14:00 is too late and 13:30 is the absolute limit.

You can also look for the sign "service à toute heure" which means that they will serve all through the afternoon. Another common (and more universally understood) indication is "service non-stop".