The two players appeared together at a news conference within minutes of Arnaldi’s withdrawal being announced.
In order to avoid Cobolli getting ill, the pair cautiously sat at opposite ends of the interview table.
Arnaldi described how he became ill on Thursday night, waking up with stomach ache at about 1am.
He said he began vomiting and was unable to sleep before calling a doctor to his room in the morning.
“It’s difficult to be here – this is not want I wanted to do,” Arnaldi said.
“I hoped it was something from dinner but throughout the day I couldn’t eat or drink and kept going to the bathroom.
“Withdrawing from a first Grand Slam semi-final is not what you wish to anybody.”
Arnaldi had spent 19 hours and 42 minutes on court en route to the semi-finals in Paris – the longest anyone has played on their way to the last four of a major since 1991.
Arnaldi apologised to the 15,000 fans, with the majority having already arrived at Roland Garros for the match.
Ticket-holders will receive a full refund, French Open organisers said.
“I feel sorry for everyone who came to watch,” added Arnaldi.
In place of the cancelled match, Cobolli held a practice session on Court Philippe Chatrier in front of thousands of fans who remained.
