Is it offensive to use ‘Saigon’ instead of ‘Ho Chi Minh City’?

I’ve heard some people talking about Saigon instead of Ho Chi Minh City. Besides the fact that those people usually were French (I’m French myself as well) I was wondering if that could be considered offensive by the Vietnamese people. As Saigon is the old name, they might feel a bit weird if someone was reminiscing about the “good old days” when Vietnam was a French colony.