the websites of museums are crystal clear that free entries for young adults are for EU residents only. It is a taxpayer benefit. Any questions like this are answered by looking at the website of the thing you want to visit. Museums in Paris are consistent; if they have a price (some are free like the Petit Palais) then they are free for those 17 and younger and for residents of the EU from 18 to 25. for monuments like the Eiffel Tower, again check their web site. the ET has a 'Youth rate' for anyone 12-24. And a child rate for those younger. Kids are not free at the ET.
No one cares if you are a student; benefits are based on age not student status.
Where you can luck out is on transport as the Ticket Jeune weekend day passes which are a huge bargain are available to anyone 25 and younger including Americans. These allow transport based on zone -- the one that covers all of Paris for a day is only about 4 Euro -- it is more of course if you get a 5 zone pass including the airports but still much cheaper than adult day passes.