The First Crusade, like the other crusades, was not organized militarily in the way that a modern military campaign would be. That is, there was no one leader who was in overall command of the Christian forces. Therefore, we cannot identify any one man who led the crusade.
In a sense, the crusade was led by Pope Urban II. It was he who called for the crusade to be launched. He was, of course, leader of the Catholic Church. However, he did not lead the First Crusade in a military way and did not go with it to the Holy Land.
The Pope did, however, send a papal legate. Pope Urban considered that legate to be the real leader of the crusade. His name was Adhemar de Monteil. Urban considered him the leader since the crusade was supposed to be about religion, not political power.
The actual fighters on the crusade were generally organized by French lords. There were four who were the most important leaders and had the biggest followings. These were Godfrey de Bouillon, who was the duke of Lower Lorraine, Bohemond, the Prince of Otranto, Raymond of Saint Giles, who was the count of Toulouse, and Robert of Flanders who was the oldest son of William the Conqueror. These men were the military leaders of the First Crusade.