In short, no, Romanticism doesn't have anything to do with the word, romance, the way we use it today.
Romanticism is a literary movement, marked by rebellion against the neoclassical, the Enlightenment, and the Age of Reason. Romanticism was popular from around 1798 to the 1830's, most specifically, in Britain. The term itself comes from Rome, or Roman.
Romanticism involves an emphasis on intuition, imagination, the personal, rebellion. It harkens back, most specifically, to medieval literature.