Nord-Atlantik-Vertrags-Organisation or Nordatlantikvertragsorganisation (NAVO) would be German.
AB is Swedish, as everything in Sweden is an Aktiebolag ;)
(Just kidding. NATO in Swedish is Nordatlantiska fördragsorganisationen, NAFO)
When NATO was formed, French was the lingua franca, and as such it made sense to put the French acronym on the logo. I suppose it's still there because they didn't want to change it.
I like the way they solved this for the global reference time standard. In English it's called Cordinated Universal Time (CUT) but in French it's called Temps Universel Coordonné (TUC).
Apparently, both sides wanted to use their preferred acronym globally and wouldn't budge. The problem was only solved by eventual agreement to use UTC, which doesn't make sense in either language, but I guess at least it's fair that way.