Actually, the First Crusade started in 1095 and lasted until 1100. But another reality check - Constantinople did not fall until 1204.
The First Crusade started because of persecution of Christians and pilgrims at Jerusalem.
Yes, the Pope called the First Crusade in 1095; 1099 was the siege of Jerusalem. However, the issue was whether Europe could have provided material aid to the Byzantines against the initial Arab assault. In the mid-7th century, when the Arabs hit the Byzantine empire, Europe was utterly incapable of sending substanive military assistance.
What does the Latin's sack of Constantinople in 1204 have to do with the Arab invasion of the 7th century?