While reading FIDE version of the rules, I stumbled upon Appendix E: Rules for play with Blind and Visually Handicapped.
There, in E2.1:
The moves shall be announced clearly, repeated by the opponent and executed on his chessboard. When promoting a pawn, the player must announce which piece is chosen. To make the announcement as clear as possible, the use of the following names is suggested instead of the corresponding letters, algebraic
A - Anna, B - Bella, C - Cesar, D - David, E - Eva, F - Felix, G - Gustav, H - Hector
Ranks from white to black shall receive the German numbers:
1 - eins, 2 - zwei, 3 - drei, 4 - vier, 5 - fuenf, 6 - sechs, 7 - sieben, 8 - acht
Castling is announced “Lange Rochade” (German for long castling) and “Kurze Rochade” (German for short castling).
The pieces bear the names: Koenig, Dame, Turm, Laeufer, Springer, Bauer.
So, FIDE recommends using Deutsch for announcing moves when tournaments with blind/visually handicapped participants take place.
A quick search did not allow me to answer the question of why is it like that and why Deutsch (not, say, French) was chosen. I also wonder, since when did those recommendations are present in the rulebook.