You seem to be referring to "Rockollection", performed by Laurent Voulzy and written by Alain Souchon. The Wikipedia article on "Rockollection" has an extensive listing (quoted heavily below) of the English-language songs that appear in the original 1977 version (of which a recording is presently available on YouTube)
"The Loco-Motion": Little Eva
Axis of Awesome "Four Chord Song".
It's not so much the same "key" ( although it is all the same key), it the same chord progression. The joke is that all of the songs consist of the same four chords.
Here is the song
(As a side note, some of the original songs are in different keys, but all transposed to the same for this song.)