Being a unabashed romantic, one of my favorite spots to get romantic in Paris is the Observatory Fountain. Its at its most romantic at night!
The Observatory fountain (featured in the movie "Gigi"), created by Davioud in 1875, is one of the most photogenic in Paris. The sculptures representing the four parts of the world are by Carpeaux (some of his works can be seen at the Orsay Museum), while the horses and dolphins are by Frémiet.