Film editor Marina Bandres Lopez-Belio and her 7-month-old son Julian Pracz-Bandres were among 150 people on board when the Airbus A320 went down over the Alps on 24 March.
French President Francois Hollande said he believed none of the passengers had survived the crash.
The family had lived in Manchester for the past seven years.
In a statement issued through the Foreign Office Mr Pracz, a post-production worker, confirmed the deaths of his wife and son.
He said: “Marina was visiting her family in Spain for her uncle’s funeral, she bought the tickets at the last moment, and decided to return to Manchester quickly as she wanted to return to her daily routine as soon as possible.
“I’m with my closest family in Manchester, and in close contact with our family in Spain at this very difficult time.”
“We are devastated and would like to request that we be allowed to grieve in peace as a family without intrusion at this difficult time.”
Condolence books have been set up in the French village of Seyne-les-Alpes, which has become the command centre for rescue teams and accident investigators.
Its is thought it could take emergency teams several days to bring the bodies down from the mountainous region.
