When Paris fell to Hitler did kaiser Wilhelm II really write to him saying "Congratulations, you have won using my troops."

He did send congratulations to Hitler, but the exact wording was somewhat different.

Via John C. G. Röhl in Kaiser Wilhelm II: A Concise Life (p. 192):

"Under the deeply moving impression of France's capitulation I congratulate you and all the German armed forces on the God-given prodigious victory with the words of Kaiser Wilhelm the Great of the year 1870: 'What a turn of events through God's dispensation!'

It is possible this has been conflated with a letter he wrote to the American journalist Poultney Bigelow in September of 1940, in which he stated:

(Same source) "The brilliant leading generals in this war came from My school, they fought under my command in the World War as lieutenants, captains and young majors. Educated by Schlieffen they put the plans he had worked out under me into practice along the same lines as we did in 1914."

edit: added page number