Venir de + infinitive is used to expressed recent past. So in this case, it means “The Frenchman […] just became a father.“
Ma chatte vient d’avoir des petits.
My cat just had kittens.
Venir + infinitive means to to come and do something
Viens voir les petits chats.
Come and see the kitties.
or to come in order to do something.
Je viens voir les chatons.
I come to see the kittens.
To go to, is be aller + infinitive.
Je vais voir les chatons.
I’m going to see the kittens.
To be going to or also is aller + infinitive.
Ma chatte va avoir des petits.
Ma cat is going to have kittens.