The Tory MP and prominent Brexiteer made the apparent threat to Sir Nick Carter as he lambasted the Ministry of Defence.
Mr Cummings, Boris Johnson's most senior aide, is understood to be planning a major reform of defence spending as he moves ahead with his bid to shake up Whitehall.
Speaking at the Defence Select Committee in the House of Commons on Tuesday, Mr Francois told Sir Nick, who is chief of the Defence Staff: "Can we just make a plea to you. You are the professional head of the armed forces.
"Please nip back to the department and ask them to sort their bloody selves out, because if not, Cummings is going to come down there and sort you out his own way – and you won't like it."
The General, who is a veteran of conflicts in Bosnia, Kosovo, Afghanistan and Iraq, did not seem shaken by the thought.
He responded simply with a wry smile.
Committee chair and fellow Tory MP Tobias Ellwood then noted: "I think that message is passed on."
Mark Francois to Britain's top general: "Please nip back to the department and ask them to sort their bloody selves out because if not Cummings is gonna come down and sort you out his own way and you won't like it"
His face says it all. pic.twitter.com/1x09w3580Q— Dan O'Donoghue (@MrDanDonoghue)July 7, 2020
Social media users responded to Mr Francois’s comments with outrage and delight in equal measure.
British actor Adil Ray OBE wrote scathingly on Twitter: “Threatening the General, Sir Nick Carter The Chief of Defence that he and his men will get a good telling off by an unelected adviser. British Politics.”
While another user wrote: “Imagine being head of the armed forces, and having Mark Francois trying to intimidate you.
“It’s like a chinuaua trying to scare a bull mastiff.”
A parody account for the European Research Group chairman, tweeted: “I can confirm that myself and Dominic Cummings will be meeting General Nick Carter for a straightener behind the bike sheds after work.”
And another Twitter user shared a screen grab of Sir Nick, writing: “His face says it all.”