from living in France / from France

  1. Since he came back from living in France, his French has improved considerably.
  2. Since he came back from France, his French has improved considerably.
    Do they mean the same?
    Thanks.

In 1, he has lived there for a period of time.
That is not necessarily the case in 2.

Presumably, you are trying to indicate that his French improved while he was in France. In which case, your sentences aren’t strictly logical. They indicate that the improvem,ent took place after the visit. Logically, something like this would make more sense:

Since he lived in France…
Since he spent time in France…

Beeesneees,

  1. Since he lived in France, his French has improved considerably.
  2. Since he lived in France, his French improved considerably.
  3. Since he had lived in France, his French improved considerably.
    Is the tense properly used in each sentence?
    Please comment and correct.
    Thanks.

I can’t tell whether it’s properly used as there is not context, however they are all possible.