Apparently an Anglo-Saxon term, but let me give you some context, this being an annotation by Wren on Sir Thomas Browne’s Pseudodoxia Epidemica (that’s the Wren BTW, Browne’s fellow member of the Royal Society).

Here’s the relevant passage of Browne, with Wren’s annotation:

Our first intentions considering the common interest of Truth, resolved to propose it unto the Latine republique and equal Judges of Europe, but owing in the first place this service unto our Country, and therein especially unto its ingenuous Gentry, we have declared our self in a language best conceived. Although I confess the quality of the Subject will sometimes carry us into expressions beyond meer English apprehensions.[2]

(2) [Wren: “That our naturall English consists for the moste parte of monosyllables, as appeares by the names of all creatures in our tongue and all our actions, and in all the parts of our bodye, exept such things as wee have borrowed from other nations. Scarce one word of ten, in our common talke, is of more then one syllable. In this very short note which conteynes 60 words there bee not above eleven (and those of Latin derivation) which are not (all of them) monosyllables.” I count 59 (different) words, of which 20 are multisyllabic, of which six are of English origin. The word “common”, though of Latin derivation, may perhaps owe its continuance in English, if not part of its derivation, to the cognate (to its present meaning) Anglo-Saxon “gemæne”.]

How accurate this is I know not but it’s the last sentence which I need some light thrown on. What exactly does he mean?

I’m on something of a Browne jag at the moment, having finally read The Garden of Cyrus or The Quincunciall Lozenge, a work which I started reading and laid down as a young man. Perhaps his least accessible piece but also, I believe, his greatest (Religio Medici excepted). The man is at white heat here, anyone who loves the English language owes it to themselves to read it. It doesn’t get any better than this!

Well, in order to keep neutrality up top, here’s the Dutch ‘Van Dale’ entry for the term ‘gemeen’, which is current Dutch (’gemeen’) for the same thing as the old word mentioned in the OP:

gemeen [meaning: common, evil or cruel] old Dutch gemeini 901-1000, middle Dutch geme(i)ne [meaning: common, general, shared]; the meaning: ‘evil’ or ‘cruel’ 1776. Old Saxon ‘giment’, old High German ‘gemeini’. Old English ‘gemaene’ [Eng. ‘mean’], Gothic ‘gamains’; beyond
Germanic Lat ‘communis’; the meaning evolved from ‘general’ to ‘normal’ to ‘worthless’ and ‘bad’; compare for similar downgrading ‘slecht’ (bad).

Afa the last element is concerned, the writer is clearly calling for comparison with the development of words such as ‘bad’ (in the sense of ‘good’) and ‘wicked’ (’great, brilliant’)

The Van Dale, when it gets the chance, is big on semantic development. But I don’t care, these kind of words tell their own story and by their very significance to society tell a tale of their own down the ages.

Browne had come to the point in his reasoning that he was about to conjecture that maybe soon, in order to learn English, her native speakers might find themselves in the position of having to first learn Latin.  From just beyond the indication of footnote[2], Browne goes on:

“And indeed, if elegancy still proceedeth, and English Pens maintain that stream, we have of late observed to flow from many; we shall within few years be fain to learn Latine to understand English, and a work will prove of equal facility in either.”

Browne is also suggesting that this would have a possible benefit: the work having equal utility in Latin as well as English.  I find this wryly humorous. 

In the last sentence of [2], Wren gives:

“...The word “common”, though of Latin derivation, may perhaps owe its continuance in English, if not part of its derivation, to the cognate (to its present meaning) Anglo-Saxon “gemæne".]"

Wren suggests that the word “common” may enjoy [edit to add: both its past and] a future in English because it has simply become common custom to use it as well as the closely related “gemæne” possibly converging in support of “common,” both words being related but not from the same roots. 

It seems to me that perhaps he intends that the language is even more “common” ie, less pure (as in gemæne, Sense influenced by “mean” (n.). Meaning “inferior, poor”) as a consequence.

And thus, I think Wren may have been amplifying Browne’s original humor. 

There is a great range of expression in the writing here.  I understand that humor is one of the most difficult things to communicate over the years and if my conjecture here is too far off the mark, possibly at least there may be something to the humor angle.