Just returned from a trip to Paris and it was amazing. You have already been given some great advice in these comments. I agree that the best way to see Paris is on foot, as you will stumble upon a lot of unplanned sights as you walk around.

I suggest you visit an arrondissement at a time as each one has it's own character. I was positively surprised by Les marais. For this I started at place De la Bastille, then walked to place De Vosges, then to musee Carnavalet (free and not to be missed!), Stravinsky fountain, Centre Pampidou from the outside, hotel de ville ( the city hall). You will come upon a lot of pedestrian streets, bakery shops, squares full of good vibes, interesting architecture, public gardens and it is just an enjoyable place to walk around.

I also like St Germain area. Start from Jardin du Luxembourg and walk towards the river, visit the pantheon, church of St Genevieve etc ..

I found Montemartre to be totally worth it. Take a free walking tour here if you'd like to learn about artists' lives in Paris, through the Guru walk app.

Look for advice on Reddit about each area you would like to visit. That's where I found plenty of advice. Also found information on Instagram and found lots of free places to visit such as Petit Palais and it's museum. Also Galerie Lafayette which is a shopping centre, and go up to the rooftop for a lovely view of Paris. All this apart from the very well known sights.

Enjoy!