It was before Mr. Connery was famous, he was war correspondent reporting from London... He fell in love with a girl there and he gets killed within the first 10 min of the movie. The girl goes to his country home and finds out he was married. What is the name of this film?

Another Time, Another Place seems to be the movie you are thinking about. Another Time, Another Place (1958) - Plot Summary

I believe it was called Another Time, Another Place and was in the late 1950's. Lana Turner and Barry Sullivan were in it. Hollywood lore says Lana Turner's real life gangster boyfriend showed up and threatened Connery with a gun. Connery disarmed him and knocked him down.