Online tutoring students/organizations based outside France without a work permit

Hello and sorry for the awfully long title, which pretty much sums up what I want to ask below! The question might be a bit stupid but I figure taking my chances doesn’t hurt either.

I’m an Indian national with a French work permit who offers online tutoring (mostly in math but also in English), and will soon obtain a micro-entrepreneur status, with which I plan to continue tutoring as a micro-entreprise. My question is: is it possible to do remote work or remote tutoring for an organization based outside France (e.g. the US, UK, China or Australia or even other EU countries) that employ mostly local tutors? Just to clarify, the question is not about whether I’d be able to tutor online - I’ve got the skills and all of my five current students are online students. The question is more about the legal side of things - e.g. can I be based on a different country (e.g. say the US) than the one where the employer organization is based in, and tutor for them as a freelance? Or do I mandatorily need a work permit for the US to be able to work from France? How about if I replace the US by other countries like China - I get an impression from my online search that they use lot of online tutors for tutoring English? Just as an added clarification - when I say tutor for an organization, I don’t mean an online learning platform like SuperProf or PrePly, with whom we don’t have to sign a contract, but rather an organization that’d hire tutors to tutor the local students.

Do you mean doing online work for overseas based companies but your bum still in France? If yes then that is fine, you just invoice the companies through your ME.

ETA this is my understanding, best to double check the official line.

I believe that’s what I meant - being physically present in France. Just to be sure about - I’m not talking about online platforms like the ones I mentioned in the OP, but rather learning centers that hire online tutors, e.g. think of an ACT training center in the US that may need online tutors.

The problem I’m facing is that I’ve applied to couple of such remote jobs, in the US and Switzerland, and the US ones rejected my applications for not having a work permit in the US, and the Swiss one didn’t bother to reply when I clarified the legal side of things? I hadn’t told them that I didn’t have an ME status as of yet, but that I’d receive it soon, but then again, they didn’t bother to ask.

A relevant question I’ve been having is that: is having an ME status enable me to bill a foreign (non-Frenhc or non-EU) company? I’ll add this bit to my post.

By the way, is ETA ‘Edited To Add’?

I think the problem arises as different countries have different labour laws, so what is ok by France may not be ok by country X. Within Europe you’ll be fine, but the States can be draconian so you need to check that from the US end.