Quiz: Remember the definition of mal de mer?
word-forming element attached to verbs to form abstract nouns of process or fact (convergence from converge), or of state or quality (absence from absent); ultimately from Latin -antia and -entia, which depended on the vowel in the stem word.
As Old French evolved from Latin, these were leveled to -ance, but later French borrowings from Latin (some of them subsequently passed to English) used the appropriate Latin form of the ending, as did words borrowed by English directly from Latin (diligence, absence).
English thus inherited a confused mass of words from French and further confused it since c.1500 by restoring -ence selectively in some forms of these words to conform with Latin. Thus dependant, but independence, etc.