From the experts:
Constance is one of the more subtle of the virtue baby names, but still has quite a prim and proper image. One impediment to its revival has been the decidedly dated nickname Connie, though modern parents might well opt for using the strong and dignified name in full.
One of William the Conqueror's daughters was named Constance, and in Shakespeare's King John, Constance is the devoted mother of King Arthur. Constance was widely used in the seventeenth century by Puritans: Constance Hopkins was a young passenger on the Mayflower.
The fictional Constance Billard School appears in TV's Gossip Girl, and Constance was the first name of the decidedly non-prim and proper Lady Chatterley.
Oscar Wilde's wife was Constance, and Mozart's spouse was the German form Constanze, nicknamed Stanzi.
Though Constance has been neglected here for a number of years, it's still ranks at Number 120 in France.
Trivia tidbit: Constance was the birth name of 1940's peekaboo-hairdo star Veronica Lake and also, not surprisingly, Connie Britton.