I have heard that many places close for Easter on that Sunday and Monday. What should we/can we do on those days? What restaurants will be open?
Like in NorthAmerica, try restaurants of a different origin : chinese, libanise, trukish, etc. In short, those which countries of origin that are not of catholic religion. It's possible that some close anyway so ask at your hotel to be sure. They will suggest restaurants nearby or in the arrondissement you will be visiting that day.
If I were in Paris around Eater Sunday i would spend it around the Basilique du Sacre-Coeur in Montmartre. When i went there last year, the tour guide told us that the bell of the Basilique du Sacré-Cœur church only rings once a year and it's on Easter Sunday (or Monday, i cant remember, please look this up). I'm not a religious person, but I think it would be very interesting to hear it since it's a very significant site, and it is one of the heaviest bells in the world.
Although I haven't spent Easter in Paris, I have spent two Christmas holidays there and though most of the local restaurants were closed on Christmas, we had an excellent Japanese dinner there, so... may be seek out a Chinese or Japanese restaurant? They typically are open during Christian holidays and may surprise you. At a Japanese restaurant near the Saint-Augustin, we had excellent food including tempura cheese - something different and definitely a French twist to typical Japanese food, yet delicious. I'm pretty sure it was the Jipangue on Rue La Boétie.
Another thought is to ask the concierge at your hotel and/or ask locals. I had probably the best French meal of my life on Easter Sunday in Bayeux, but it was because I'd asked ahead what was good and what would be open and booked it.
It's a family holiday, French families will go out to celebrate as well, so the restaurants that are open will most likely be crowded and may have special and more expensive menus.
As for things to do, many museums and the Eiffel tower are generally open, but may be insanely crowded. Book ahead for tours and tickets. Easter is a really busy time in Paris. It might be interesting to look into any processions or special things going on in Sainte-Chapelle or at the Notre-Dame de Paris and see those since they are special. See if there is something unique going on just for Easter.
There are also beautiful parks if the weather is nice. How about a walking tour - enjoy the town. Sometimes you find the best treasures just walking.
Mentioned in this answer: