The French c is French, which is the culture with the most-consistent and strongest claims to Celtic heritage.
In German, it’s kelte, same sound as Irish c and Greek kappa.
Maybe we should leave the distinction irrelevant. From the author himself, “ in the nineteenth century many of the scholarly breakthroughs were made by German scholars, who were recognised to be the leaders in this field. Many of them also harboured sympathy for the Celtic regions of Brittany, Ireland, and Wales, and thought they should be freed from French and English imperialism.” And that’s how the word became popular in 1930s Germany.