I'm not sure how this would work. Perhaps you would first need to define the term "regular employee." In the U.S. the best way to define a regular employee is by the tax form. Generally a regular employee is considered a W-2 which means you have to do things such as pay into that employees social security (and other social programs) among other things. If your employee isn't a W-2 then he/she is generally a contractor.
Since an Indian citizen doesn't live in the U.S. then none of these sorts of laws apply. So, from the U.S. perspective, you would simply be a contractor and your services would be a tax write-off.
You specifically mentioned you aren't asking about companies which have a business in India, so that's out.
Conclusion: I don't know about Europe but I imagine it's the same as the U.S. Because you don't live in the U.S. you will always be a contractor and the only tax / legal implications is that payments towards your services are a write-off. You would be a regular employee in name only. You wouldn't necessarily receive any of the benefits that typically go along with the status of "regular employee."
Since an Indian citizen doesn't live in the U.S. then none of these sorts of laws apply. So, from the U.S. perspective, you would simply be a contractor and your services would be a tax write-off.
You specifically mentioned you aren't asking about companies which have a business in India, so that's out.
Conclusion: I don't know about Europe but I imagine it's the same as the U.S. Because you don't live in the U.S. you will always be a contractor and the only tax / legal implications is that payments towards your services are a write-off. You would be a regular employee in name only. You wouldn't necessarily receive any of the benefits that typically go along with the status of "regular employee."