A man named Samuel De Champlain claimed New York.
No it was not claimed by the French
This area was first claimed by Holland.
Samuel de Champlain
The colony of New York included what is now Vermont. Upon the creation of the US, Vermont was not a state but it was not a part of New York State either. It was its own country for a short period of time, then it was admitted to the Union was a separate state. It was never claimed by nor a part of New Hampshire.
Samuel de Champlain
The New York area was originally claimed by the Dutch in the early 17th century when they established a settlement called New Amsterdam on the southern tip of Manhattan Island. This claim was formalized by the Dutch West India Company, which sought to capitalize on the lucrative fur trade. In 1664, the English seized control of the area and renamed it New York.
The area claimed by New York and New Hampshire primarily includes parts of present-day Vermont and New York. The dispute over this territory was settled in the late 18th century, leading to the establishment of Vermont as a separate state in 1791. Today, Vermont, New York, and New Hampshire are the primary states associated with the historical claims of these two states.
Henry Hudson
New Hampshire was claimed by Vermont, Massachusetts, and New York.
Henry Hudson
Henry Hudson, an English navigator working for the Dutch East India Company, claimed the New York area for the Dutch in 1609. Hudson sailed up the river that now bears his name and established a trading post for the Dutch.
The French claimed New Franc, hoping they could make a colony. They also wanted more fur for business.