A paragliding partner who witnessed the tragedy immediately alerted Chamonix search and rescue.
Mr Cooke was pronounced dead by emergency service workers when they eventually reached the site.
The Chamonix News reported Cooke was an experienced paraglider who was well equipped at the time of the accident.
Following the tragedy his grieving partner, Dani Evans, who ran a bed and breakfast with Cooke for international guests, paid tribute to the Kiwi on Facebook.
"My everything - from the moment I met you until my very last breath on this Earth I will keep you just like I promised. I love you now and forever my bub. Always."
Consular assistance has also been offered to members of the family.