Please reassure me about basement french drains
Well, a (concrete slab) floor is just a floor, supported by its substrate. You may have some subsidence afterwards, so I'd advise my tips here, especially the one about undermining it a little to lock it all in place once you re-pour. Rebar is a must.

Done right*, I have no concern for the foundation. I'd be worried that there's a pocket under the slab somewhere and a section might drop a little. But that's not a show stopper, it's just more work.

*AFAIK, done right means you don't dig below the bottom level of the foundation.

If the slab is keeping your foundation from collapsing, your house has some big problems.