PARIS—A man carrying the deadly SARS-like novel coronavirus entered the intensive-care unit of a hospital in northern France on Sunday, while officials in Saudi Arabia announced two more deaths linked to the virus, as international health authorities scrambled to understand how it spreads.

The 51-year-old man became France's second confirmed case of the virus after sharing a hospital room in the northern town of Valenciennes with the country's first case, a 65-year-old man who had recently traveled to the United Arab Emirates....