By whom? Well it was the combined armies of Europe that took to the first Crusade, but mostly Normans and Franks. Godfrey became known as the first King of Jerusalem (he refused the title, but after his death his cousin Baldwin had no such reticence, he was made lord of Edessa and ruled his Armenian Christian subjects); Raymond of Toulouse thought he would be the leader of the crusade, but he became lord of Tripoli (a singularly remarkable man). Bohemund had already bowed out of the Crusade when governance of Antioch was given to him and the Normans, but his cousin Tancred came along and became Prince of Galilee.
THAT is who captured Jerusalem (yeru = city, salem = peace; so Jerusalem is the ‘city of peace’ showing that HE is not without a sense of irony).