I've seen and heard, in particular jazz musicians, count in using "un" instead of the regular pronunciation of the word "one". It seems unlikely there's a technical or practical reason for this, but I'd love to find out why it's done. Thank you.
When playing jazz, I will often count in by calling attention to "the one" with a propulsive or percussive syllable: "mmm", "uhh", "nnn", etc. Sometimes it's to emphasize the one; sometimes it's to communicate the primacy of beats two and four; sometimes it's a concession to being a trumpet player and needing to prep for the first notes.
Overall, though, it's more a stylistic convention, an idiom, than having any specific technical or practical reason. One band leader I've heard often counts in "a-one a-two a-you know what to do".
Un just happens to be French for 'one', but it's doubtful that's a reason it's used. It matters not what gets used. Billy Joel used 'uno dos tres quattro', a band I work with uses 'un deux, trois, quatre'. One band I used to work with simply grunted: 'ugh, ugh, ugh ugh ugh ugh' in place of '1, 2, 1 2 3 4'.
As long as everyone knows what the count in means, that's sufficient. In fact, whole orchestras manage to come in on time with nothing like that. Simply an upbeat (usually) of the conductor's baton. So why a 4 piece band needs two whole bars, I've yet to find out..!
There's a military tradition of counting beat one, or the lead off step, differently - most people are familiar with "HUP two three four". The difference emphasizes the first beat, and uses a syllable that can easily be said loudly (similar to the way Ten-Hut! has replaced Attention! in the US).
The use of drums in popular music derives partly from the way they are used in military marching, so it's possible that part of the reason is that the tradition has carried over.