I'm thinking of telling my wife's friend that she's being a bad friend.
How is she being a bad friend to your wife?
She's being extremely jealous of a new purse I bought her.
If someone in your spouse's social circle is treating your spouse badly, it's okay for you to call out that behavior and support your spouse. A marriage is a serious relationship and it's expected that spouses watch each other's backs and support each other as best as they can. If you notice someone treating your spouse badly, you should try to find ways of getting that person to change that behavior and to start treating your spouse nicely again.
I'm going to ask the friend if it's her fault for my wife's poor attitude towards me.
That is a good start, to get to the root of the problem, talking is paramount. If you can persuade your wife's friend to be a better friend and ask her why she is so upset, then it would solve the drama between you and your wife.