With a twenty-year age difference and his constant womanising, I'm guessing divorce divorce divorce. I doubt either of them would have got much out of it.
Depends how long it lasts, really. If she doesn't conceive and he still goes on to marry Marie de' Medici after Elizabeth's death, having the same children, then all we have to think about are the political consequences - internationally and at court - of that alliance. Especially as once Elizabeth settles on a husband, she loses a significant bargaining chip.
What would be their motivation for marrying each other?