I think the main thing I would say is not to feel like you have to cram too much in. Paris is one of those cities that just screams "I'm in Paris!!" wherever you go, so just walking around is great.
We spent quite a bit of time walking along the Seine, had a look at poor old Notre Dame and read the boards about the rennovations, Tuileries and Luxumbourg gardens were both good for having a walk and a sit down - and it'll be warmer now so you can get lunch and have a picnic - not particularly French, but we got filled bagels from the Bagelstein close to the Tuileries and ate them as we walked.
The transport is great and the T+ tickets work for both the metro and the buses (and the little funicular up to Sacre Coeur) - we went on buses quite a lot as you could sightsee a bit more, and found using Google Maps was as good as anything to let you know what bus/metro to take, plus changes and times. Each ticket is valid for 90 minutes so covers you for any changes. A "carnet" of 10 is the best way to buy them if there are enough of you or you're making enough journeys - there's also a child's ticket and you can get them in 10s as well. You can also use contactless I think but I was struggling to work it out so we just bought paper tickets from the machines in the end.
Another lunchtime eat - apparently there's a brilliant falafel place L'As du Fallafel on 34 Rue des Rosiers. There will be queues but they move quickly. My friend raved about it but we didn't make it there.
We did make it to Bouillon Chartier for dinner one night. It's v cheap and an amazing art nouveau atmosphere. Another queue but watching the incredible queue management is part of the fun and it moves v quickly.
A bit more expensive, we also went to Cafe du Commerce (on Rue du Commerce - be careful with Google maps which has listings for other places with the same name) which is also v friendly and a gorgeous setting. We went for lunch and had the fixed lunch which was delicious and good value - it felt vv French and fancy while still being family friendly.
Both have a website so you could see whether it's for you.
Have fun!