This "M. Meyniel" is indeed, and definitively, Henri Meyniel (sometimes spelled Henry Meyniel). Note that the article you mention was communicated by Berge, at a time (1972) when Meyniel was still a very young, and little-known, researcher. This explains the use of the "M." to talk about Meyniel. Note also that on the following pages, the author is just called "Meyniel", without "M." nor "H.".
Meyniel then became a recognized French graph theorist, though very few is known about his personal life; a rare photo of him can be found in this article by Baird & Bonato :
In this other article (probably his last, even posthumous, publication), we learn that Meyniel was affiliated to CNRS (French national scientific research center)... and that he passed away in 1995. Actually, he commited suicide (mentioned here). His obituary tells us he was born in 1950 in a small town near Bordeaux, Caudéran.
(These informations had been confirmed to me when I was doing my thesis, from personal communications, for example with my PhD advisor, Frédéric Maffray, a co-author of Meyniel in his last article.)