There are several entries in Wikipedia claiming that the Garoutte and d'Espinassy families had ancestors from the French Royal family, particularly Henry IV, (see below). Furthermore, there were two similar claims by Ellan Douglas Thiesen, in her book "The French and American History of Michael Garoutte and His Descendants" (1974). According to the first claim, an American Garoutte descendant (Leo Haskett) traveled to Marseille in 1939, where a French Garoutte told him that he was a descendant of the French Royal Family (page xxii). According to the second claim, we get the following excerpt from page xxxv:

"It seems that Michael was brought before the King, Louis XVI, for engaging in a duel when dueling had been forbidden by the Court, on pain of death. When the King saw that it was Michael (his cousin), he simply waved him away with a command not to do it again."


Wikipedia

Wikipedia

Wikipedia

After doing some research, I believe that these claims were wishful thinking by some Garoutte descendants in America because none of the other search results I found provided any Royal ancestor. While the Garoutte and d'Espinassy families were certainly among the French nobility with titles (eg. baron), important positions in society (eg. captain, attorney general), and property with land, going back for many centuries to the 13th century or before, I do not believe that they had any Royal ancestors. Such an important detail would not have been overlooked.

Catholics and the American Revolution, Vol. 3 (1907) page 342 Martin Ignatius Joseph Griffin.

Daughters of the American Revolution Magazine (1908), Volume 32, page 60.

The American Catholic Historical Researches (1909) page 271.

Iron in the Pines, The Story of New Jersey's Ghost Towns and Bog Iron (1957) page 204 Arthur Dudley Pierce.

Histoire h�ro�que et universelle de la noblesse de Provence. Tome premier (1757) page 342 Artefeuil.

Illustrations europ�ennes... Livre d'or de la Noblesse, Volume 4 (1846) page 178 Le Marquis de Magny.

Dictionnaire historique et h�raldique de la noblesse fran�aise, r�dig� dans l'ordre patronymique, d'apr�s les archives des anciens parlements, les manuscrits de d'Hozier et les travaux des auteurs, contenant un vocabulaire du blason, la notice des familles nobles existant actuellement en France, avec la description et le dessin de leurs armes Volume 1 (1895) page 1125 Camille Philippe Dayre de Mailhol.