The topic has been brought up before, for example in the thread below:
Rayman CUE/BIN causes speed problems

However, some of the information there appears to be inaccurate / incomplete, so I decided to share my findings.

I've experimented with all 4 Rayman DOS games - the original, as well as Designer aka Gold, "By its fans" aka Forever, and Collector. They all appear to have the same issue:

The Issue

• With DOSBox set to core=auto and cycles=max, the game speed goes crazy, switching between normal and too fast (the effect is like fast forwarding a VCR), making the game basically unplayable.
• Real CD versus image does not seem to have anything to do with it. I've experimented with both, as well as with CD-ripped versions that do not use the CD at all. Behavior is the same.

It's been suggested that the game has speed problems on real hardware as well, so it should not be considered a DOSBox-specific issue, however it is greatly exaggerated in DOSBox with the above settings. On real hardware it may exist, but is typically not as intrusive.

Workarounds

• Setting cycles to some fixed amount seems to work well. The actual amount may be machine-dependent. The recommended value of 25000 worked well for me (on a fast Core 2 Quad).
• Setting to core=normal also seems to work well.
• Changing from 60Hz to 50Hz in the game's menu does not work. Not consistently, at least (may work in some setups).

For the original Rayman only, there is another thing that works - in the main options menu, the graphics mode should be set to PCI2/VESA (the slower modes) instead of PCI1 (fastest). This may be equivalent to changing the DOSBox machine from svga_s3 to vesa_nolfb, as was suggested in the thread above. However this has the side effect that in the first level of "Eat at Joe's" the darkness effect will be disabled (entire level is illuminated, instead of just Rayman's fist). So, in a way, this can be used as a cheat for that level. The expansion packs do not have this setting in their technical options menu.

Overall, because of the simplicity, the preferred workaround, is to change the DOSBox core type / cycles. This can be done either from the config file or the DOSBox command line (so you can do it via the batch file that changes the mode, launches Rayman, then restores whatever setting you want).