The English translation of Pierre Gilliard’s Memoirs quoted by Sarushka is incorrect : in French he wrote the Tsarevich received the « grand cordon de la Légion d’honneur » which means the sash of the Order. Only the Knights of the highest degree (Grand Croix /Grand Cross) wear one, along with a gold breast star. Knights who receive the badge of one of the 4 lesser degrees wear it with a ribbon instead of a sash. Although the name of Alexis (nor of his father) doesn’t appear on the list of foreign recipients found on Wikipedia, various sources state that both of them did receive the highest French decoration.
Regarding the Tsarevich, I found some interesting information in Part 4 of the Memoirs of Raymond Poincaré (President of the French Republic from 1913 to 1920) entitled « Au service de la France » (At the service of France). He writes that during his July 1914 State Visit to Russia (as Pierre Gilliard recalled) he was invited at the Alexandria-Peterhof Lower Palace for a private luncheon with the Imperial Family. Amongst the gifts he presented on Wednesday July 9/22, was a complete desk set for Alexis to whom he also bestowed, in the name of the French Government, the Grand Sash of the Legion of Honor, made to a smaller size than usual as he was still a child.
As why a young boy would receive the highest decoration France could give, the same as a Head of State, it seems that some Foreign Sovereigns and Crown Princes did received the same (Grand Cross). According to a Russian source, Nicholas II got his Grand Cross on May 6, 1884 (on his 16th birthday when his coming of age was celebrated). Given the close relationship that had developed between France and Russia under Alexander III, which led to the Franco-Russian Alliance, no doubt Alexis would have received the same honor for his 16th birthday too. But President Poincaré writes that, a few weeks before his departure for St. Petersburg, the French Ambassador to Russia had urged the French Government to award the Grand Cross of the Legion of Honor to the Tsarevich during his visit. At first, Chairman of the Council of Ministers, and Foreign Minister, Viviani (who was to accompany Poincaré to Russia) hesitated as he was thought Alexis was too young to receive such a high honor. Apparently he wasn’t alone, as when the Council of Ministers took a vote on the Ambassador’s insistent request, the decision passed by a one vote majority only. In early Summer of 1914 there already were rumors of War and the purpose of President Poincaré’s trip to Russia was to strenghten the Franco-Russian Alliance while trying to prevent a generalized conflict in Europe. The French Government probably decided that granting the Tsarevich its highest decoration at that point in time would be seen as a token of enduring friendship.
So this is how Alexis received the French Legion of Honor. At the time, no one knew that World War I would start only a few days later and that if the French had voted to wait until Alexis was 16 to award him the Legion of Honor, he would never have received it…