I couldn't find a birth record for John Michel's son John Lewis Michel (Dec 15, 1890, Philadelphia). So no help there for a birthplace for John Sr.
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I found John L with his maternal grandparents in Norriton, Pa, in 1900. but his mother is not there. He is listed as John L Mitchel, age 9. Grandparents are Mathias, 69, and Kunigunda, 60.
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Also, here are some records from the Philadelphia City Directory which might help you determine when John Michel arrived in Philadelphia, and maybe in the USA. Also to figure out when the family broke up:
1875, 1878, 1879, 1880 Philadelphia City Directory
no John Michel at all
1881 Philadelphia City Directory
John Michel, shoemaker, home at South 22nd corner of Pine
I skipped 1882 to 1889
1890
John Michel, shoes, 2417 Ridge Avenue
1895
John Michel, shoes at N 26th corner of Montgomery. home at 1901 Judson Place
1896
John Michel, shoes, 2430 Ridge Avenue
1897
no John Michel, shoemaker
1898
no John Michel, shoemaker
1900
there were 4 men named John Michel. none were shoemakers
skipped 1901 to 1908
1909
John Michel, clerk for the Pennsylvania Railroad, home 1810 N VanPelt [note: the son]
there were 8 other men named John Michel. none of them was a shoemaker