As a Champion of France, he won a match against Champion of Belgium, Alberic O'Kelly de Galway, (2.5 : 1.5) in December 1938.Gromer played for France in Chess Olympiads:
In 1930, at third board in 3rd Chess Olympiad in Hamburg (+4 –6 =1);
In 1931, at second board in 4th Chess Olympiad in Prague (+3 –9 =4);
In 1939, at second board in 8th Chess Olympiad in Buenos Aires (+6 –4 =7).In September 1939, when World War II broke out, Gromer, along with many other participants of the 8th Chess Olympiad (Najdorf, Stahlberg, et al.) decided to stay permanently in Argentina.
He won at Buenos Aires (Bodas de Plata) 1940, followed by Franciszek Sulik, Carlos Guimard, etc.
He took 7th at Aguas de Sao Pedro/São Paulo 1941 (Erich Eliskases and Guimard won).