Le Roy entered the École Normale Supérieure in 1892, and received the agrégation in mathematics in 1895.
He became Doctor in Sciences in 1898, taught in several high schools, and in 1909 became professor of mathematics at the Lycée Saint-Louis in Paris.
In 1919, Le Roy was also elected a member of the Académie des Sciences morales et politiques.
Along with Henri Poincaré and Pierre Duhem, he supported a conventionalist thesis on the foundation of mathematics.
In the domain of religious dogmas, he rejected abstract reasoning and speculative theology in favour of instinctive faith, heart and sentiment.