Theres plenty of things to do in Paris and I wont bother listing them, theres already a lot of content about that.
As for weekend getaways, the train system from Paris to elsewhere is good enough that you can almost visit all the main cities in the country.
Some I would recommend
>Lyon
>Bordeaux
>Strasbourg
>Saint-Malo
>Vannes
>Reims
>Rouen
>Dijon
>Lille
You could also go for a day to places like
>Versailles
>Fontainebleau
>Chantilly
>Giverny (Monet's house)