Unfortunately, the answer is no. A first class relic is defined as a part of the body, and since she was burned at the stake, no remnants of St. Joan of Arc's body can be found. The authorities instructed the executioner to scatter Jeanne's ashes to the winds, so there would be no chance of a relic remaining to inspire veneration by the people. [Source] (http://unamsanctamcatholicam.blogspot.com/2011/06/are-there-any-relics-of-joan-of-arc.html)

Since she was considered a heretic, the English gave her no proper burial, so her grave is lost. There is an interesting story about her heart: despite repeated attempts to complete the incineration, the English executioner found that Jeanne's heart would not burn. He is quoted as saying, "I have burned a Saint!" He scattered her ashes from the ancient bridge, replaced by the Pont Boiëldieu in 1896. There, he threw her heart into the waters of the River Seine, and it became one with the Heart of France. [Source] (http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=22152)