Administrative division is a term for an administrative region within a country that is created for the purposes of managing of land and the affairs of people. The area typically has a local government with a certain degree of autonomy, and is on a level below that of the sovereign state.

https://en.wikipedia.org/wiki/Administrative_division

Wikipedia's suggestion to leave it in FR is one option. We can also use circle since it means "a territorial or administrative division or district"

Circle
7: a territorial or administrative division or district
The province is divided into nine circles.
https://www.merriam-webster.com/dictionary/circle

Lower Saxon Circle
https://en.wikipedia.org/wiki/Lower_Saxon_Circle



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Note added at 1 day 1 hr (2020-09-30 09:38:54 GMT)
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Circle is currently used in other countries that have English as their official language (India).
https://wokha.nagaland.gov.in/admin_hq.htm

and is translated by cercle in FR (despite cercle not being used in France)
https://fr.wikipedia.org/wiki/District_de_Tawang

Personally I'm ambivalent about leaving this untranslated. I'm not even particularly keen about not translating the term Département, but I do it because it's the widely imposed convention, and English-language readers are expected (supposedly) to know what this is in a French document about France.

You can't have that expectation here. After referring to Wikipedia we see that a Cercle is an area which is one step smaller than a Région, which translates fairly uncontroversially as "Region", with a bit of luck.

Leaving it in the French (and in italics? and with an explanation in square brackets the first time it is mentioned?) seems to me to give the reader too much to puzzle over. A "sub-region" does what it says on the tin. It's very prosaic and boring, of course, unlike Cercle, which is rather groovy and idiosyncratic. A groovy translation might be "Shire", "Bailiwick" or "Canton".

However, I doubt whether this my answer will find much favour.

Territorial unit widely understood to be between a region and a municipality/parish/commune/etc.

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Note added at 10 hrs (2020-09-29 18:30:47 GMT)
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"cercle" is itself a translation of the Arabic "daa'irah", which the new Oxford Arabic-English dictionary translates as "area/district" generally and "constituency" or "jurisdiction" in specific contexts.

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Note added at 7 days (2020-10-06 20:13:01 GMT) Post-grading
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Have been wondering whether the Arabic "daa'irah" is not in fact a translation of the French "arrondissement" that seeks to capture the "rond" part. On the other hand, why would Morocco have then translated this Arabic translation back as "cercle"?