French forces in Germany had regular military registration, but on a red background, often with an additional FFA. An E or an S (Services) may precede the serial number, often starting with 998. Since about 2005, the E (Economats) vehicles have a 00-1234 format, either in silver on blue, or white on black background. Such plates have been seen on SFOR vehicles. 

      

     

Private vehicules of military forces in Berlin had a distinctive FZ (Französische Zone) followed with a  4 digit serial number. Just after 1954, they were on a green background (CW) or had GMB (Gouvernement militaire de Berlin) on a black background.
See also
German Forces in France, and former NATO forces in France.

       

Private vehicules for troops located in other regions than Berlin have blue plates, in which the second digit represents :
1= Baden-Baden, 2=Freiburg, 3=Landau-Pfalz, 4=Trier, 5=Villingen-Constance, 6=former-Tübingen (end in 1977), 7=Reutlingen. In July 1999, most of french troops left Germany, but in several places (1, 4 and 5) Eurocorps french-german troops replaced them and still use these blue plates.