To show off

He's showing off to impress her. frimer, se la pêter (très familier)

show [sth/sb] off (display proudly). montrer, exhiber, mettre en avant

• When his famous mother came to school, he showed her off to all his friends.

show [sth] off (draw attention to). mettre en valeur

• He bought a close-fitting shirt that showed off his newly developed muscles.

For my English speaking friends:

In French "alors heureuse" is a joke to mock men thinking that they are sooo irresistible that their presence is enough to make a woman happy ;=)