The Proto-Indo-European root is *ǵenh₁- "to give birth, beget".
The "birth" meaning being extended to cover familial relationships, the suffixed zero-grade form *ǵn̥h₁-yo- (the *-yo- suffix meaing "of or belonging to") became Proto-Germanic *kunyam "family", then *kuninǥaz "king", Old English cyning, and English king.
The form *ǵn̥h₁-sḱo- became Latin gnāscī, nāscī "to be born". This combined with com "together" (from *kom- "together, with") to form cognātus "by common descent" - and cognate. Cognates are words that have a common origin. Some people define cognates as words that have a similar sound and meaning - but cognates can often be very semantically and phonologically divergent, as this blog shows.
In Latin, the suffixed form *ǵenh₁-es- became genus "type", which gives us words like gender, generation, and genre, thru French. In Greek, *ǵenh₁-es- became γένος genos "race, kind", which gives us gene.
The form *ǵn̥h₁-ti- (*-ti- was a nominal suffix) became Latin gēns, gentis "race, clan", then gentīlis "of the same clan", then Old French gentil "noble". This was borrowed into English as gentle c 1200. Then around 1600, French gentil "nice, pleasing" was borrowed into English as jaunty, spelled to resemble the French pronunciation.