@CrniRi,
The movies name is "Locke"
However, you have quite a number of things mixed up about it. I only knew the answer because I enjoyed it so much.
It's not French. It's British.
The woman giving birth is not his mistress. It's a colleague he had a one night stand with.
He regrets it, and doesn't have any feelings for her.
However, it's important for him to be at the hospital for the birth of the baby, because his own father abandoned him, and he vows not to do that.