Upvote:-2
If you are from a non visa required country, you can enter into the France as a visitor for up to 3 months with a valid reason. Otherwise you need to apply for a visa if you want to travel before your work permit starts.
Upvote:-1
Typically, you cannot have two different visa for the same country at the same time; the second approval would invalidate your first visa. So your plan doesn't work.
Instead, apply for the work visa for a month earlier, with the perfectly ok reason you have.