Hi Is 10 days enough to see the hi-lights in Paris and then travel to Bordeaux or Provence for a couple of days and back?
No. No. No. No. (is that 10 characters?)
Spend 5 nights in Paris, then take the TGV to Provence or Nice for 5 nights. Fly home from Nice. Going back to Paris is a needless back-track.
It depends on how much you'd like to see in Paris, what pace you travel at and how much time you spend in museums. For some people 4 days would be enough of a big city and they'd be ready to move on to somewhere smaller. I have not been to Bordeaux or Provence for that matter. For many, Bordeaux would not be as high on the list of France cities than others. If you are looking at wine regions and will have a car, I'd choose Loire, Burgundy or Alsace before Bordeaux. Whether you can fly out of Nice for your return to home would depend on your budget and your home city.
I will also comment that many on the forum have the time and also the budget for longer stints in Europe and tend to spend longer periods of time in places that younger people with less vacation time might. I would watch some of RS tv shows and clips on France to decide how to allocate your time.