The question of who was influenced by what is more of a historians’ bedtime game than a solvable problem.
There certainly was an international community of scientists and inventors who closely followed one another’s experiments and successes. These were reported in publications like Scientific American, first published in 1845 and originally a clearinghouse for news on advances in technology, in scientific journals, and in major newspapers.
France was perhaps the leading country for advances in invention and technology at the time, probably ahead of even Britain, with the U.S. catching up fast at the end of the century. Their newspapers were even more likely to report on progress than ours, and French inventors were even more likely to write books on their notions.
But the whole process was also a bit haphazard. If you didn’t speak French you could miss out on many reports that didn’t get translated. Local inventors sometimes got noticed by local newspapers but without a national press syndicate (the Associated Press started in 1846, but with only four newspapers) many reports never circulated widely. Or were read even if so. The Wright Brothers flight did make The New York Times almost immediately, but was treated more as yet another report of flight, one of many that people were always making with who knew what evidence to back them up. In October of that year, for example, Samuel Langley, head of the Smithsonian, had a widely publicized failure of his attempt to be the first to fly. A report of a couple of bike sellers in North Carolina wouldn’t attract much credibility.
It’s more important to understand what was in the air, pun intended, at the time. Everybody was trying to build a powered heavier-than-air craft in 1903, and balloonists, glider enthusiasts, and dirigible builders had shown the way, while theoreticians provided much better technical understanding than ever before.
For this thread, the idea of sending, recording, or playing back sound was also an ancient one, and people were attempting it seriously about as soon as the telegraph was publicly introduced. The word phonograph dates back to 1863, from a paper tape system. People approached it by adapting various existing technologies. Edison himself was experimenting with the acoustic telegraph in 1875, trying to send audio waves over the wires.
Edison could have had any number of predecessors or approaches in mind when he began work in 1877, including people who he might have seen as competitors at the time but are forgotten today because they never got anywhere.
I’m somewhat jaundiced about who did what first, in the same way I went into the does sf make predictions thread to say that people can and do make their definitions so loose that anything can be the predecessor of anything else that resembles it in any way.
None of this diminishes in any way what Scott de Martinville accomplished. I’m just saying that the approaches were so different that trying to draw a direct line between them doesn’t lead anywhere. Somebody always fails first, just as somebody always succeeds first, just as somebody always makes it truly successful first, with lots of room for argument every step of the way.