I've heard about various foreigners fighting in the American Revolutionary War, notable ones being the Marquis de Lafayette and Casimir Pulaski. I just recently learned a little bit about Tadeusz Kościuszko after seeing a statue of him in Boston and that led me to look into other Polish people who supported the American side in the revolution, including Michael Kovats and (EDIT: My bad, Kovats was Hungarian) Haym Salomon.
I can understand why the French supported the American Revolution - it hurt the British and they had colonial ties to North America - but why were there so many Poles involved?
American Revolutionary war 1775-1783
https://en.wikipedia.org/wiki/Partitions_of_Poland 1772(First) 1793(Second) 1795(Third)
In short many Polish people were force to run away from the country when Participation happen.
Poland was semi Democracy (Aristocrats chose King), have constitution https://en.wikipedia.org/wiki/Constitution_of_May_3,_1791.
American were seen as brother in spirit with freedom/brotherhood narrative, that want break free from big and powerful king. We where losing country, you were fighting for your own country...
Also Kościuszko return to Poland because he created uprising in 1794 after second partition. So some may see this as training practice.
https://en.wikipedia.org/wiki/Ko%C5%9Bciuszko_Uprising
Plus French support you, and many Polish people run to France. So I imagine France encourage Polish veterans to help USA.
Summary: Timing, similar ideologies/ideas and France.