This is an old thread by now, but I found a good source of information on the origins of the Fonda family, including the Marquis (Baron) de Fonda of 1400's Italy.It appears in the book "Early American Families" by Rev. N. A. Williams on p. 24:
The Renselaer-Bowier papers say that (1) Douw Fonda was a Frisian. and Tacitus says that the Frisians dwelt along the coast of the North sea. They were converted to Christianity before A. D. 800. The family of Fond, was originally from the Republic of Genoa, Italy. The Marquis de Fonda was one of the leaders of a revolution in Genoa, having for its object the overturning of the aristocratical government, and putting the election of the Doge and Senate, into the hands of the people at large. The Doge (=duke) was the duke, or chief magistrate. Our ancestor was an early republican, and must have lived there, between 1339, when the first Doge was elected , and 1528 when the Dogate ceased. Baron de Fonda was unsuccessful in his attempt, and fled from the country, taking refuge in Amsterdam, Holland, whence his descendant, Jellis Douwese Fonda, emigrated to America in 1642, and had grants of land from the Dutch government, settling in or near the present city of Albany, N. Y. There is a perhaps less credible tradition also, that the Fondas were Huguenots, and fled from France to Holland after the massacre of St. Bartholemew's night, Aug. 25, 1572. There is another tradition that they fled from Spain on account of persecution or followed the Duke of Alva to Holland. It is also said that they belonged to the royal house of Spain, fled to Italy, because of religious persecution, and came later to Holland. Possibly they fled from Italy to France, and from France to Holland. The form of the family name is Latin, and therefore similar In French, Italian, and Spanish, indicating the Latin origin of the family, probably in Italy.
The Fondas were Dutch Reformed Protestants when they emigrated to America, and must have been among the first converts of the Reformation. Their descendants are widely scattered throughout the Union, though many are still living near the old home in Eastern N. Y.
The family name is taken from a deep valley in the Apennines, about 12 mi. from the city of Genoa, called Fonda, a name which means bottom, deep, foundation, &c. it is said that, In the early part of the last century, the estate was still in the possession of a branch of the family, the Count de Fonda, and there are many of the name,