That’s a curious find. My reading of the reverse is as follows, with letters I can read in red and my guesses for the other letters in black:
NÉ A
PESSARO EN 1792
MORT A
PASSY EN
1868
So, in French, that would be “Born in Pessaro in 1792, Died in Passy in 1868”. That would fit as a commemorative medallion for the Italian composer Gioachino Rossini (Joachim Rossini in French). He was born in Pesaro, Italy (French spelling Pessaro) in 1792 and died in Passy (an area of Paris, France) in 1868.
I can then persuade myself that the bust on the obverse is of Rossini himself and that it says “ROSSINI” to the right. On the left it may say “GIOACHINO” or, more likely, his French equivalent Christian name “JOACHIM”.
Can’t find your exact medallion, but here’s a portrait of the man from another medalet:
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