My friend forgot a brooch in the car, so I wanted to send a message to her
You've been forgotten your brooch in the car.
is it correct?
In my experience, it's not natural to use "forget" here. Native speakers would naturally say:
"You've left your brooch in the car."
If you really wanted to use the verb "forget", you could say:
"You forgot to take your brooch when you got out of the car."