In Dune, why is a single Fremen called Fremen and not Freman?
Does the word have nothing to do with men? (In pure grammar context)
Because "Fremen" has become a proper name with time.
Does the word have nothing to do with men? (In pure grammar context)
Yes, it was originally "Free Men" - in the early concept for Dune, they were convicts who worked in spice harvesting in exchange for a reduction in their sentence. Frank Herbert then changed this to make them an indigenous people, and turned "Fremen" into a proper name for them.
The backstory in the prequels (written by Herbert's son based on his notes) retcons this, with origin of the name as "Free Men", a group of escaped slaves thousands of years before the time of Dune.
You can make up reasons why the people's name would be a bastardization of an English term when their language is based on Arabic (e.g. the man who came up with it spoke English but most others spoke Arabic, so that became their language and they kept the name because they liked it but then forgot its meaning). Ultimately it's just an artifact of the creative process.