You already know that J’ai apporté une veste means I brought a jacket. To say that you didn’t bring a jacket, make sure you add pas after ai!
Je n’ai pas oublié mes chaussures.
I didn’t forget my shoes.
Il n’a pas acheté de billet de train.
He didn’t buy a train ticket.
Elle n’est pas arrivée.
She hasn’t arrived.
Je paye can mean I’m buying or I’m paying.
Nous payons les courses.
We are buying the groceries.
Tu payes le taxi.
You are paying for the taxi.
Elle paye le repas.
She is buying dinner.