Translation:Louis is bald, so he doesn't comb his hair.
That would make much more sense. However, as I pointed out ages ago, there is a difference between being classed as "bald", which in the UK is usually taken to mean having a bald patch of an unspecified extent and being totally bald, ie with no hair at all on the head. In the former case there is generally a need occasionally to groom around the periphery whilst in the latter case perhaps only a spit and polish is required :-D
As other commenters have indicated, this is a ridiculous sentence. If he doesn't have hair, "his hair" makes no sense as a translation -- plus, "cheveux" isn't in the French sentence. "He doesn't comb" is a complete and correct translation. Of course, it doesn't make much sense. In English we would say, "so he has nothing to comb." Fix it, Duo!
Although "cheveux" isn't in the French sentence it doesn't need to be because "se peigner" means "to comb one's hair" - see here: https://www.collinsdictionary.com/dictionary/french-english/se-peigner You're right about it being awkward in English, however as I pointed out previously, lots of "bald" people have hair around the periphery that they may or may not choose to comb! :-D
I was sort of thinking this but even still it doesn't really make sense like that because this implies he couldn't come someone else's (like his child's) hair. My first though as to how I would say this clearly unnatural English sentence was: "...so he doesn't need a comb". This still may run into the same problem but I feel like if I said this in this context with my friends people would know I mean just for him, but if I said just "...he doesn't comb hair" people would still be confused and find it unnatural.