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The -h- in Old French supposedly is from influence of Frankish *hoh "high." The -n- perhaps is due to association with Provençal enansar, enanzar "promote, further," from enant "before, rather," from Latin in + ante "before."
common suffix of Latin origin forming nouns, originally from French and representing Latin -mentum, which was added to verb stems to make nouns indicating the result or product of the action of the verb or the means or instrument of the action. In Vulgar Latin and Old French it came to be used as a formative in nouns of action. French inserts an -e- between the verbal root and the suffix (as in commenc-e-ment from commenc-er; with verbs in ir, -i- is inserted instead (as in sent-i-ment from sentir).
The stems to which -ment is normally appended are those of verbs; freaks like oddment & funniment should not be made a precedent of; they are themselves due to misconception of merriment, which is not from the adjective, but from an obsolete verb merry to rejoice. [Fowler]