I don't know if this is connected or not -- the birthdate for Jean Nicolas Jr is 21 Oct 1820, rather than 19 Oct 1819, and it's not clear if this one ever left Europe. The Moselle civil records are not on line, or weren't the last time I looked, but the TD are. This is from a Geneanet search and shows a Jean Nicolas Gross who x to a Madeleine Biebel. Madeleine was from Wittring, Moselle. There is a distinct lack of place names in this tree and the references are sometimes a little cryptic. But Wittring is only about 4 miles from Herbitzheim.
Index page for the search is here: https://en.geneanet.org/fonds/individus/?go=1&nom=biebel...
There are 2 or 3 other entries for the same Madeleine on the page, some giving more data on Nicolas, including his birthdate in Wittring and the names of his parents. NB that the first Nicolas apparently died, since there was a second son of the name b 1828, shown on the trees lower down the page (the first one on the list shows Jean Nicolas as 1820-1881, the only child named on that tree). Bruno Gabriel's tree says this family emigrated to NY in 1832 "with their 7 children," though I wonder if they actually brought 2 Nicolases. According to Gabriel's tree, all of the children were born in Wittring, with specific dates given.
You have to sign up for an account to use Geneanet. It's free, painless, and allows you to search the family trees until the cows come home -- they're the most useful part of the site and I'm in them most days of the week looking for clues. There are pay sections of the site, but the trees are freely available for research.
Hope this helps some. From the locations, dates, and circumstances, it seems highly likely that this data refers to the same family you're searching.