Here are the two best guesses that I have found are Lucien Laurent and Eugène Maës.
Laurent made history in Uruguay by scoring the first ever World Cup goal: a volley in the 19th minute of a game against Mexico on July 13, 1930. France won the game 4-1, but lost their remaining group matches to Argentina and Chile, and were thus eliminated. Laurent was ruled out of the third game due to injury. He was the only surviving member of the 1930 French team to see France lift the 1998 World Cup on home soil, and died seven years later at the age of 96.
Eugène Maës was the first true goalscorer for the French national team. With a great combat injury during World War I which obliged him to retire from professional football, Maës would certainly have been one of the best players for the tricolors, because in less than two years of his international career, he scored 15 goals in just 11 caps. His most glorious day remains March 17, 1912 in Turin, where, against Italy, after having arrived at 5 A.M., he scored a hat trick, and the French team defeated the Italians for the first time in their history, 4-3. The Red Star striker also holds another record with the blue shirt, thanks to the 5 goals he scored against Luxembourg in 1913, in an 8-0 victory. Only Thadée Cisowski would equal this accomplishment in 1956.