Exit Schengen temporarily before student visa

Hi! I’m a Mexican citizen and I’m going as an exchange student to France, I got my long-stay French student visa (type D) about a month ago. However, my family planned a trip to Germany, the Netherlands, France, etc., weeks before.

I understand that I can't enter with my long-stay student visa before it's validity begins (a few days before the semester starts), so I'll have to enter Germany as a tourist with my passport. But I do need to leave Schengen Zone in order to re-enter as a student with my long-term visa.

My question is: could I travel to the UK in order to leave Schengen Zone and re-enter France just about the time the validity of my visa starts, or do I have to return to Mexico to travel again to France to enter with my student visa?

I'd really appreciate your help and suggestions, I know this is so messed up, we should've planned this much better.