The Digital Rights Management (DRM) software in this program
prevents it from running in CrossOver. If you are in a legal jurisdiction
which allows removal of such software, you may have luck running this
program. Unfortunately, CodeWeavers, because they are subject to the
Digital Millennium Copyright Act, will be unable to support you.
However, paulthetall sounds like he got it working with the CD - although I don't know how that could work.
(The ratings are from advocates, the CodeWeavers rating is "untested")
It's also possible that there are some legal pay-for download versions of the game that don't have CD based copy protection. Steam doesn't have BF1942, only BF2. Though even if there are some it won't help you since you already bought the CDs.
It's also possible that some game update tightens or softens the CD check.