How can a doctor request training in major hospitals outside his country?

He needs to write to whatever department it's called in France to a school he'd like to attend to find out if his credentials meet France's medical criteria. In Canada, in the school, that department is called the Dean of Medicine. In the country, it's called the Royal College of Physicians and Surgeons. They will look at where he trained and assess whether his training meets their requirements. They will advise him if he has to take classes to meet their specifications. Once that is done, he needs to contact the head of the specialty he wants to train in (oncology, paediatrics, etc) and see if there are any fellowship or subspecialty positions available.

Or, he could start with the Specialty Head and be redirected from there. But he will likely have to go through all these steps and it could take a couple of years.

I would suggest he discover which countries are desperate for what he wants to specialize in and contact them as well.