You're likely going to need to consult with two experts: An arborist and a foundation expert.
If roots have made it under your floor, the foundation is likely compromised to some extent. You'll want someone out there to see how much. If the house was built on a slab, you might be OK and it could be repairable.
As for the tree, the problem is that it's too close to the house. If removing the tree isn't an option, you can maybe somehow cut all the roots on that side, dig a trench and then install some form of root blocker.