OK so not exactly an activity, but you nevertheless need to experience the metro in Paris. It makes it easy to get around, is clean, efficient and quintessentially Parisian. It is also the best metro in Europe (and maybe the world). In Paris you are never more than a 10 minute walk from a metro stop. Watch for pickpockets.
Tickets are available at vending machines and some staffed windows – machines have English instructions. Single tickets are (currently as of 1/2020) 2 euros and a carnet of 10 costs 15 euros. You can now also buy a multi day pass called the Pass Navigo which is useful for a week and adventures further afield (weekly pass 23 euros plus 5 euro one time fee for the card). The Paris Visite pass is only useful if you plan on extensive city travel as it may not be as good a deal as a carnet.
To use the system pick up a map at any station. Lines are color coded and numbered – directions are by the end of the line stop. Transfers within the system are free. Put your ticket in the turnstile, retrieve it and enter. Hold onto the ticket – you may need it to exit or if asked to see it by a fare inspector. When you get to your destination follow the sortie (exit) signs.