Additionally, some CDs may have region-coding, which is a type of digital rights management (DRM) that prevents them from being played on players from other regions. If a Japan CD has region-coding, you may not be able to play it on your English player, even if your player is region-free.
To determine if your CD player is region-locked or if a CD has region-coding, you can refer to the player's manual or the CD's packaging.