There is a record of a Jean [John] Maillard and three children arriving by way of London on the ship Peter and Anthony, which carried French refugees to America in 1700. Also, a John and Peter Mallard are listed as residents of the Huguenot settlement at Manakin in Virginia. A Pierre [Peter] Mallard is listed in the 1720 vestry book for King William Parish, Virginia.
I am trying to locate my ancestor, Mary Mallard, who may be related to the above people. She was born circa 1749 and was reportedly a French Huguenot (i.e., French Protestant). In 1775, she married Samuel Arrowsmith, Jr., in Baltimore. The family moved first to Pennsylvania, pushed on to Kentucky, and finally settled in Ross County, Ohio. Could your Peter be her brother?