"I will be learning French when I return to the city" or "I will learn French when I return to the city"? Which sentence is correct if I want to say I will start to learn it (I was lazy until now)? I guess, it is the second sentence, but I doubt. Is it correct to use another one if I want to say I will renew my learning process when it will be possible?
They have subtly different meanings, but both are correct.
"I will be learning french" means that you will start to learn french again.
"I will learn french" Implies that you are going to learn the whole language. This is still correct, but it has a different meaning.
Please note that people sometimes say "I will learn" when they mean "I will be learning". In practice, you can use them interchangeably since people will work out the meaning.
On another side note: "I will be learning french for 4 months" and "I will learn french for 4 months" Have exactly the same meaning, since you have given a time scale. "I will learn french for 4 months" no longer suggests that you expect to learn the whole language, which is why they are equivalent.