The -ment(e) Suffix in Romance Languages
In Romance languages, the -ment(e) suffix, which is used to form adverbs, is etymologically derived from Latin.
People who spoke Vulgar Latin used to say words like clara mente (with a clear mind, i.e., clearly) etc. to form adverbs. The Latin word mente is the singular ablative case of the feminine noun mens (mind in English). So the word that goes along with the -mente suffix has to be feminine as well. With time, the 2 words became 1 word. Knowing these facts, we now know the reason for which feminine adjectives are needed to form adverbs in modern Romance languages.
Examples
slowly
French: lentement from the feminine version of the adjective lent (slow in English)
Italian: lentamente from the feminine version of the adjective lento (slow in English)
Note
In Romanian, there is a main way of forming adjectives that is different from what we have talked about here.