During a heated debate, Mr Self claimed every racist and anti-Semite in the country “probably voted for Brexit”.
Hardline Brexiteer Mr Francois demanded: “How do you possibly know that? I think you should apologise.”
Mr Self replied: “To who? Racists and anti-Semites?”
Mr Francois said the author had tried to slur every Leave voter as a “bigot”. He then asked: “You were in every polling station looking over everybody’s shoulder when they voted?”
It prompted Mr Self’s terrifying stare. While presenter Jo Coburn moved on to other guests on the panel, Mr Self locked eyes with Mr Francois as the pair gazed at each other in a similar manner to boxers at the start of a bout.
The tense stare-off led Rob Burley, the editor of the BBC’s live political programmes, to remark: “I’ve worked in telly for 23 years and I’m not sure I’ve ever seen anything quite like it.”