Mandolute is just the English name given by the U.S. manufacturer Weymann to this instrument.

I know it, in French, as "un mandole" (not to be mistaken with "une mandole" which is a mandola) or "un mondole".
From online doc, it looks like "un mandoluth" seems to be common as well and has the advantage to be unambiguous.

Thus, I recommend to use "mandoluth" as primary French alias, "mandole" and "mondole" as other French aliases.
Kabyle spelling most probably is "mondol" but I am not sure about it.

Note that Wikipedia pages currently are a bit of a mess about this instrument:

• both https://en.wikipedia.org/wiki/Mandole and https://en.wikipedia.org/wiki/Mandolute refer to this same instrument,
• https://fr.wikipedia.org/wiki/Mandole does not link to this instrument but to the mandola (mandolin alto).