Notes

There's a lot to say apart from very generic advice (be aware of the specific laws for each country because they can differ a lot, especially on drugs issues, respect the fact that, even if Europe is the closest to the US you'll find in the world on a cultural point of view, you will face cultural shocks...), so I'll try to keep it short.
Obviously if you're going travelling all across Europe, you will probably stick to Paris if you're visiting France at one point of your trip. As already said, be polite, say Bonjour, even if it sounds exotic or just a cliché, it's one of the rare true things about France, be aware that the French are not the best in spoken English in Europe (for multiple reasons) and that even with young people you'll have to be patient, be aware that (and especially in Paris) people will look not as welcoming or open as you could imagine, that's just how we behave, we don't like to show how we feel in public places or to foreigners, so don't take offence at that.
Paris is a great place when it comes to sightseeing (even Parisians do it, I do it myself) but that's what you'll find on any Tourists' Guide. For anything else, there are nice places around both banks of the city, so check these neighbourhoods for example:
Right Bank (northern part) : avoid the West past the Arc-de Triomphe (no monuments, no bars, only ridiculously rich, uptight and boring neighbourhoods), and North-West, except maybe the Batignolles (unless you plan to start a family there). Montmartre is ok for sightseeing (though a bit overrated imho), but beware of tourist traps.
Paris Northeast is not what most people imagine (no-go zones and shit) but you don't have to romanticise it as an alternative traveller either, this is not a very interesting area of the city for travellers, and you don't have to like it or to see it just for the "exoticism" or whatever. Gentrification is doing its job though, so if you like hipster bars, they will mostly be there.
If you go a bit to the South, you will find yourself in the 10th and 11th arrondissement, along the canal St Martin, or around the Place de la République and Place de la Bastille. These are all hotspots, especially at night. Try there. Day or night, you should try the Marais, it's cool and the "LGBT+ spot" in Paris.
The Seine quays are nice almost everywhere, but I strongly recommend you the part named the "Jardin Tino-Rossi", between the Austerlitz train station and the Jussieu university. It can get really crowded and fun on summer nights.
The Left bank (south of the Seine) is better to experience during day-time (unless you like empty streets), because most of the Universities are there.
The Quartier Latin can be quite nice (avoid the Rue de la Huchette and Boulevard Saint Germain which are tourist traps, and run to the Rue Mouffetard, place de la Contrescarpe, go and check the Bouquinistes for cheap books for a few euros, especially Rue des Écoles). Unfortunately, the cafés names you might have in mind (Flore, Balzac, Procope, idk) are not what they used to be and are now outrageously expensive for very low odds of running into a Jean-Paul Sartre or a Michel Foucault...
Underrated monuments:
The Great Mosque of Paris (5th arrondissement, near the Jardin des Plantes)
The Hôtel-de-Ville (I really like the architecture)
The Bibliothèque Nationale François-Mitterrand (13th arrondissement)
Underrated neighbourhoods:
Paris' own "Chinatown" around the Place d'Italie
Montparnasse and the Rue de la Gaîté
Try the parks, especially the Parc Montsouris or the Buttes-Chaumont (they are pretty much the same so choose one), and the graveyards.
More unusual parks include the Jardin d'Agronomie Tropicale (far in the Bois de Vincennes, almost out of the city limits, don't go there unless you have a lot of time because you'd want to see more of the Bois de Vincennes), you'll find the relics of the French Colonial Exhibition. Closer to the center, I really like the Jardin Alpin inside the Jardin des Plantes (5th arrondissement), go there at 10 am, and use the tunnel entry inside the the enclosed garden that stretches between the great greenhouse (if you have money, check that up) and the closed "ecological garden".