I can't help with Visa questions, but we were in Paris this past fall with my kiddo (who just turned 5), and also did a trip to England when he was 17 months old, so I remember the toddler travel days well!
For restaurants, I would recommend trying to arrive right when they open. We found most restaurants opened at 12 - when we arrived shortly thereafter, we were the only ones there, but by 12:30 or 1 the place was packed and was turning people down. Because of our early bedtime, we tended to eat lunches out and dinners in our Airbnb. A few times, we did eat dinner out, but given the French tendency to have hours-long meals, it occasionally meant we were still at the dinner table at 9pm!
This past trip, we used the Paris metro some, but primarily used the buses. Google maps on your phone has a bus feature that makes them so easy. And it's much more fun to be above ground watching the world go by than in a dark tunnel crammed in a metro car. If you're bringing a stroller, be aware that not all metro stations will have elevators. We did Uber occasionally, but tried to avoid it because we didn't have a car seat.
Our kiddo loved the Ludo Jardin playground in Luxembourg Gardens, seeing the Eiffel Tower, and looking at all the Christmas displays in the big department stores. Depending on when in November you go, you might be able to see them too. We had planned to do a day trip to Versailles, but ended up not going because we just needed a day to chill. I know my son would have loved the gardens and Petite Trianon though! With a kid, that would probably be my focus over the main palace, which gets very packed.
Sorry, I can't help with the visa questions. Have fun!