Working as an auto-entrepreneur and being employed by another company?

I am moving to France in October. I have had an offer of part-time employment (20hrs per week on minimum wage) with a French company teaching English to children after school. I plan to take this position because I think it will make it easier to learn French and make new friends. However, my current company (in the UK) has offered me the chance to do freelance editing work for them as well. This would be great for me as it means I would have a bit more income. Would I be able to set myself up as an auto-entrepreneur and work freelance for them, while also working as a part-time employee of the French company? Is there some guidance somewhere on how to go about this if it is possible?

Also, I was only really planning to do freelance work for my current company because I don’t really have the contacts to get work in other companies, and I wouldn’t have time to do more work for other companies anyway. I have read on other parts of the forum that it is important to have more than one customer. Would this apply to me here? I wouldn’t be working regular hours or using the company’s equipment or in a clear line of authority so would it be OK for me to have just the one company freelance, especially given that I have another position in France?