Air France was founded in 1933 and is the flag carrier of France. The Air France nickname of “Air Chance” has been cited in print in 1952, 1957 and 1958 and is still used by some today, although flying has become much safer than it was in the 1950s.
 
   
Wikipedia: Air France
Air France (formally Société Air France, S.A.), stylised as AIRFRANCE, is the French flag carrier headquartered in Tremblay-en-France, (north of Paris). It is a subsidiary of the Air France-KLM Group and a founding member of the SkyTeam global airline alliance. As of 2011 Air France serves 35 destinations in France and operates worldwide scheduled passenger and cargo services to 156 destinations in 91 countries (including Overseas departments and territories of France) and also carried 59,513,000 passengers in 2011. The airline’s global hub is at Paris Charles de Gaulle Airport, with Paris Orly Airport, Lyon-Saint Exupéry Airport, Marseille Provence Airport, Toulouse Blagnac Airport, and Nice Côte d’Azur Airport serving as secondary hubs. Air France’s corporate headquarters, previously in Montparnasse, Paris, are located on the grounds of Paris-Charles de Gaulle Airport, north of Paris.
 
Air France was formed on 7 October 1933 from a merger of Air Orient, Air Union, Compagnie Générale Aéropostale, Compagnie Internationale de Navigation Aérienne (CIDNA), and Société Générale de Transport Aérien (SGTA).
   
Google Books
Enlightening:
Letters 1946 - 1960
By Isaiah Berlin
London: Chatto & Windus
2009
Pg. ?:
(7 August 1952—ed.)
It was an Air France – Air Chance is a better name – aeroplane, & there was no pretence about women & children.
 
Google Books
A Persian Spring
By Wilfrid Blunt
London: Barrie
1957
Pg. 11:
“Air France, Air Chance.”
 
Google Books’
My East Was Gorgeous
By Ira J. Morris
London: Travel Book Club
1958
Pg. 46:
You travel Air-Chance, not Air-France, or you can go British Overdue Airways flying in one of their Super-Cancellations. T.W.A. are Try Walking Again and S.A.S. are S.O.S.
 
20 February 1974, Omaha (NE) World-Herald,  “Fly by Airplane, Fly Aeroflot” by John Dornberg, pg. 33, col. 1:
A few years ago, for example, after suffering a series of crashes in quick succession, Air France acquired the nickname “Air Chance.”
     
Google Books
The Head in the Soup:
A Novel
By Peter Levi
London: Constable
1979
Pg. 182:
“But you had better go by El Al not by Air Chance.”
 
Google Books
Consumer Revenge
By Christopher C, Gilson, Linda C. Cawley and William R. Schmidt
New York, NY: Perigee Books
1983, ©1981
Pg. 282:
Air France was nicknamed “Air Chance” for many years, reflecting well-publicized difficulties in keeping its flights aloft, but has now been accident free (as of this writing) for several years.
     
Google Groups rec.humor
Fly if you dare !!!
B|rge Haga
7/2/91
(...)
AF AIR FRANCE Air Chance
 
Google Books
Black Box: The Air-Crash Detectives—
Why Air Safety Is No Accident
By Nicholas Faith
Osceola, WI: Motorbooks International
1997
Pg. 44:
Among the more obvious have been Air Chance for Air France, Air Fungus for Air Lingus, and Better Off on A Camel for the late lamented British Overseas Airways Corporation.
 
Google Books
Experimenting on a Small Planet
By William W. Hay
Berlin: Springer-Verlag
2013
Pg. 236:
I jokingly told Don that the airline had earned the nickname Air Chance.