In reading, I often see "pa fouti," such as "M pa fouti di ou ki kote li te ale." Is "pa fouti" vulgar or inappropriate in certain contexts? (noticing that "fout" might be a root)

No, it's not vulgar at all.

fouti (use in negative sentences) means to be able, can, also to dare

M pa fouti pale.
I'm not able to talk.
I'm unable to talk.

Mwen malad.  Mwen kouche, mwen pa fouti leve.
I'm ill.  I'm laid down, I'm unable to get up.

Mwen te si tèlman sezi, mwen pa't fouti di yon mo.
I was so shocked, I couldn't say a word.

M pa fouti di ou ki kote li te ale.
I'm not able to tell you where he/she went.

Li pa fouti fè frekansite sa yo lè pwofesè a la.
She dares not do all these impertinences when the teacher is here.
She dares not be that bold when the teacher is present.
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words