First, I'm aware that this film has a fair few historical innacuracies, none the less...
The film depicts large megaphones attached to the exterior of their Sherman tanks. Would they have had a method to actually play music on board a tank at the time? I'm guessing lacquer phonograph records would skip like crazy on board a tank underway, to say nothing of firing the main gun. I don't think magnetic tape recorders/reproducers were even available yet. But possibly they could have gotten their hands on some military hardware I don't know about?
See a relevant scene here: https://www.youtube.com/watch?v=lELZMc7mvgw
Magnetic tape recording was available, and commercial recorders appeared in the 1930s. However, it was largely confined to Germany, and didn't escape into the wider world until after WW2.
However, the ancestor of magnetic tape recording, magnetic wire recording, had been around since the end of the 1800s. It wasn't common, but there were commercial recorders available, with 1 hour reels of recording wire, so this is a possible technology. Wire recorders were used by the sonic deception units in the US "Ghost Army" (simulating the sound of military activity by large units to keep enemy units committed to non-useful parts of the front line). (Wire recording only really hit the big time after WW2, just in time to be replaced by magnetic tape.)
The other possible recording technology is optical, where the acoustic signal is encoded as varying transmission of light through a strip of film (either by varying the gray level, or the width of a transparent sound track). This was common in the movie industry, with popular formats appearing in the 1920s. The technology is older than that, for example having seen military use in WW1 for recording the sound of artillery firing for the location of enemy batteries as I discussed in https://www.reddit.com/r/AskHistorians/comments/8tx04n/did_canadians_at_vimy_ridge_use_a_type_of_radar/
As for playback, self-propelled sound systems had been around since the 1920s (e.g., the first RG Jones sound truck, made in 1926 by R. G. Jones, the founder of the still-operating RG Jones (see http://rgjones.co.uk/docs/about/history.shtml for some of their history), and this US political advertising sound truck https://commons.wikimedia.org/wiki/File:Political_campaign_sound_truck_1940.jpg from 1940). The above-mentioned Ghost Army use sound trucks (with speakers of rather substantial size and power like this and this (the boxy thing on top of the halftrack is the speaker unit), and this).
Of course, the movie might just assume that they have a movie-magic vibration-proof phonograph/gramophone/record player.
