The girl's name Pulcherie (POOL-sher-ee) is rare worldwide. See this link for recent French statistics. In ancient times the name was known due to Saint Pulcheria (this spelling pronounced pool-KAY-ree-uh), also known as Roman Empress Aelia Pulcheria. Her name means "beautiful," from the Latin word pulcher, pulchra. From the same root word we get the name of the Caesalpinia pulcherrima, seen above, which is a flower in the family of pea plants and is native to the American tropics such as the West Indies.
Aelia Pulcheria ruled the Roman Empire during the Byzantine Era as regent over her brother, Emperor Theodosius II. She became Augusta and took a vow of chastity but when her brother died Pulcheria married and became Empress. She died three years later, becoming a saint. During her reign she held a great deal of power, including religious influence and patronage/commissions.
While Pulcherie is rare in France it is even more rare in America, with no more than 20 people nationwide named Pulcherie, likewise for Pulcheria.