It features newly recovered scenes of a kiss sequence from her performance of Sleeping Beauty which was initially seen during a live transmission on December 20 1959.
Darcey Bussell will present a programme for BBC4 which looks back at the Royal Ballet performance, called Fonteyn '59: Sleeping Beauty, which be broadcast on March 7.
There had been fears that nothing had survived from the second part of the performance as when researchers opened the appropriate canister, they found a duplicate of act one had been left inside.
But after months of searching through archives, they came across six film cans labelled "A Rolls" and discovered the one surviving copy of the second part of the performance.
The new film is part of the Spring Ballet Season of programmes to be screened on BBC2 and BBC4 in early March.