Though you might think that Paris is crazy expensive and you can't afford it, you definitely can if you do it right.
There's no point in staying in a super fancy hotel room since you'll rarely be in your room (unless this is a trip where you want to splurge – then you're probably reading the wrong article for your trip).
Paris has a ton of free stuff to do. The museums (even the Louvre) offer several free days throughout the year. Paris is also known for hosting many free concerts, and many of the historical monuments cost nothing at all to visit.