In August 1954, the French parliament voted 264:319 against the treaty about joint European armed forces. In the other countries of the treaty (BeNeLux, Italy, West Germany) the parliaments had agreed to the 'European Defence Community' before, but without the French approval the whole project failed.
Originally it was the French PM Pleven who suggested such a joint army in 1950. During the Korean war the U.S. had given up their policy of a demilitarized West Germany. The young Federal Republic should now contribute to the defence of the West. Her European neighbours also saw this nescessity but still feared a rearmed Germany.
So PM Pleven suggested to create a European army which would use and control German armed forces at the same time. The German chancellor Adenauer became a big supporter of this idea while the Americans got more and more sceptical and impatient as the negotiations among the Europeans took quite long.
After the final failure of the 'European Defence Community' West Germany built up national armed forces. She joined the NATO in 1955 what was then the pretext of the Warsaw Pact's founding.
So what would have been different if the French parliament had approved the joint European army in 1954?