Could I travel for example into Germany as a US citizen (= on an US passport), and not tell them that I am a French citizen too? Or this a violation?
If the passport you're using has a visa requirement, you would usually have to list any other nationalities (not just passports) on the application form. Making incomplete statements is a lie.
If the passport you're using has no visa requirement, you won't be asked.
As David pointed out in his comment, a French citizen (with or without passport) cannot get a visa for Germany. He has a right to enter with just his national ID card and to stay as long as he doesn't do anything to get himself deported. And getting deported would be extremely difficult, ordinary crimes or stupidity are not enough.