December (n.)
c. 1000, from Old French decembre, from Latin December, from decem "ten" (from PIE root *dekm- "ten"); tenth month of the old Roman calendar, which began with March.

The -ber in four Latin month names is probably from -bris, an adjectival suffix. Tucker thinks that the first five months were named for their positions in the agricultural cycle, and "after the gathering in of the crops, the months were merely numbered."
If the word contains an element related to mensis, we must assume a *decemo-membris (from *-mensris). October must then be by analogy from a false division Sep-tem-ber &c. Perhaps, however, from *de-cem(o)-mr-is, i.e. "forming the tenth part or division," from *mer- ..., while October = *octuo-mr-is. [T.G. Tucker, "Etymological Dictionary of Latin"]