Maybe it needs a valid label.

According to Ubuntu, the CD label should be RayQuiz_HF (I'm not running a standard version of Rayman, but its core remains the same) so I did this:

mount e /media/cdrom0 -t cdrom -label RayQuiz_HF

I started the game, but it still couldn't find the Rayman CD. Is my syntax wrong perhaps?

Not sure. Try uppercasing the label - RAYQUIZ_HF.

I've had no luck with that either. 🙁

Here's something that might help: I know that the in-game music is not stored as data on the CD. Instead the music is stored as audio tracks, which means that I can play the in-game music on just about any CD player. Does that require additional modules to be installed? I know that Rayman needs MSCDEX (> v2.1) in some way or another. I should also mention that I got a warning when mounting the CD saying that "mounted subdirectories are not fully supported yet" (version 0.65 as retrieved from the Ubuntu repositories).

Try making a bin/cue image (ISO won't work because it doesn't support audio tracks) from your original disks and mount it in DOSBox using its internal imgmount command (see the readme file for details).

0.65 ?? Try to find 0.70 or even better 0.71.

I did this:

imgmount e /home/pdedecker/Desktop/rayman.bin -t iso -fs iso

That partially worked. The game, the graphics, the sound etc. work fine except for the fact that I don't hear the in-game music. Can that be fixed (I just want to get the best gaming experience possible 😀) or is that too complicated?

Hmm - sure you have the cue-info available too? Do you have a /home/pdedecker/Desktop/rayman.cue file? If so, mount that instead of the bin-file.

Whoops, I used the .bin file. I checked if the in-game music was working, but instead of the music I got to hear a loud noise as if it was a data track.

Here's a piece of information that might help you solve the problem: if I put my Rayman CD in my CD player, I have to skip track 1 because it is a data track. The other tracks are normal audio tracks.

Here are the contents of the .cue file in case you need them:

FILE rayman.bin BINARY TRACK 01 MODE1/2352 INDEX 01 00:00:00 TRACK 02 AUDIO INDEX 00 12:18:71 INDEX 01 12:21:06 […]
Show full quote

FILE rayman.bin BINARY
TRACK 01 MODE1/2352
INDEX 01 00:00:00
TRACK 02 AUDIO
INDEX 00 12:18:71
INDEX 01 12:21:06
TRACK 03 AUDIO
INDEX 00 14:24:05
INDEX 01 14:26:06
TRACK 04 AUDIO
INDEX 00 16:30:65
INDEX 01 16:32:67
TRACK 05 AUDIO
INDEX 00 18:31:64
INDEX 01 18:33:66
TRACK 06 AUDIO
INDEX 00 20:39:58
INDEX 01 20:41:61
TRACK 07 AUDIO
INDEX 00 22:47:17
INDEX 01 22:49:20
TRACK 08 AUDIO
INDEX 00 24:35:49
INDEX 01 24:37:54
TRACK 09 AUDIO
INDEX 00 26:38:31
INDEX 01 26:40:35
TRACK 10 AUDIO
INDEX 00 28:30:29
INDEX 01 28:32:31
TRACK 11 AUDIO
INDEX 00 30:38:38
INDEX 01 30:40:41
TRACK 12 AUDIO
INDEX 00 32:35:60
INDEX 01 32:37:62
TRACK 13 AUDIO
INDEX 00 34:37:62
INDEX 01 34:39:66
TRACK 14 AUDIO
INDEX 00 36:06:09
INDEX 01 36:08:11
TRACK 15 AUDIO
INDEX 00 38:07:25
INDEX 01 38:09:27
TRACK 16 AUDIO
INDEX 00 40:32:16
INDEX 01 40:34:20
TRACK 17 AUDIO
INDEX 00 40:42:65
INDEX 01 40:44:67
TRACK 18 AUDIO
INDEX 00 41:42:63
INDEX 01 41:44:65
TRACK 19 AUDIO
INDEX 00 43:37:58
INDEX 01 43:39:60

I cannot send you the .bin file for legal reasons and because it's 450MB in size.

The problem is in the bin/cue image.

Try another program to create the image, i.e. UltraISO.

Have a look to this thread:
Rayman with noise instead of CD music [SOLVED]