Month names collection / metastudy

[Koen G]

The circumflex first appeared in written French in the 16th century.

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Wait, this is important, right? In the same Wiki article, mai is even given as an example of a word that would need the circumflex. The idea is that these were once diphthongs (in pronunciation) but had now become only digraphs (in writing) that were pronounced as a monophthong vowel. So something that was formerly pronounced as English "may", in French became something like English "meh". (Very approximately). 

In other words, the use of the circumflex in "may" matches that of Jacques Dubois and presumably other grammarians writing in the 16th century. If this is true, the earliest dating for the month names is the first half of the 16th century.