The 'ment' in 'government' has nothing to do with Latin 'mens' - it's a suffix that's hanged on to verbs to make a noun with a meaning related to the verb. Here's more than you ever wanted to know about the suffix, courtesy of the OED:
-ment, suffix forming ns.
Originally occurring in adopted Fr. words in -ment, either representing Latin ns. in -mentum, or formed in Fr. on the analogy of these by the addition of the suffix to verb-stems. The Latin -mentum was added to verb-stems, and the resulting ns. sometimes expressed the result or product of the action of the verb, as in fragmentum fragment, and sometimes the means or instrument of the action, as in alimentum aliment, ornāmentum ornament. In late popular Latin, and hence in French, the suffix, while retaining its original functions, came (through sense-development in some of the older words) to be also a formative of nouns of action. In AF. the suffix was still more frequently employed than in continental OF. Of the many words in -ment adopted into English from French, some have concrete senses, as garment, habiliment; the majority are nouns of action, as abridgement, accomplishment, commencement. In most of the instances the Fr. verb has been adopted into English as well as the n. derived from it. Hence the suffix came to be treated as an English formative. Early examples of its use as appended to native English verb-stems are onement (Wyclif's rendering of L. unio), and hangment (in the Promptorium c 1440 given as the equivalent of L. suspendium, suspencio). In the 16th c. the suffix was very freely added to English verb-stems, not only to those of Romanic etymology (as in banishment, enhancement, excitement), but also to those of native origin; examples of the hybrid formations of this period still surviving in use are acknowledgement, amazement, atonement, betterment, merriment, wonderment. Since the 16th c. many new derivatives in -ment have been formed from verbs of obvious French origin. Among verbs of native English etymology, those with the Romanic prefix en- (em-), and those with the native prefix be-, seem to have given rise to derivatives of this form with especial frequency: examples are embankment, embodiment, enlightenment, entanglement; bedazzlement, bedevilment, bedragglement, bereavement, beseechment, besetment, bewilderment. Of formations in -ment from other native verbs there are few instances since Shakespeare's time. It is rarely that the suffix has been appended to any other part of speech than a verb, as in dreariment, funniment, oddment.
The letter y (after a consonant) ending a verb is changed into i when the suffix is appended, as in accompaniment.