Unfortunately, no biographical details can be investigated about the hornist P. Melchior. Four of his composed works had been printed. It is the "Trois grand Duos concertants pour premier et seconde cor" op.2, 3 duos concertant op.3 for2 horns and the  volume with once again 3 duos op.4.
The music is dedicated to "Monsieur le Comte Cormiev du Medic" who was employed by the French military music. This is described on the print as "Capitaine commandante au troiseme Regiment de la garde Royale".
P. Melchior’s biography is illuminated a little by the third print, assumingly his first printed work, without opus number, with the title
„Trios grand trios concertant pour trios cors en Mi ".
The trios are dedicated to Frederic Duvernoy ("par son Eléve" P. Melchior).
So, Melchior probably studied in Paris at the Conservatoire with Duvernoy.

Duvernoy was born in Montbeliard on 16-10-1765 and came 1788 as a hornist to the orchestra the Comedie-Italienne. He changed 1797 to the Parisian opera. 1801 together with other solo players, he was relieved of normal opera service in order to be able to attend better to the solo tasks. At this time, he was a teacher at the Parisian Conservatoire de Musique. Duvernoy created the "Cor mixed" type of playing, by which he propagated the almost exclusive use of the middle register of the horn. Duvernoy was pensioned in 1816 and died on July 19th, 1838 in Paris.
Because of these information, one can accept an appearance after 1815 for all three publications of P. Melchior. The trios were printed in the Pariser publishing house Henry Lemoine in cooperation with the Parisian publisher David.