In fact it probably wouldn't be too far off the mark to say they share a mutual dislike for each other - and they aren't afraid to show it.
So Dati's attack on her former boss over his statement that after the defeat (and apparent departure from political life) of Nicolas Sarkozy there was no natural leader in their centre-right Union pour un Mouvement Populaire (Union for a Popular Movement, UMP) party hardly comes as a surprise.
|Rachida Dati (screenshot BFMTV-RMC radio)|
Fillon's comment was without doubt a salvo fired in the direction of the party's secretary general Jean-François Copé and a means for him to set himself up as a potential successor.
But it was too much for Dati who, not mincing her words, was more than willing to give her take on what he had said when she interviewed by Jean-Jacques Bourdin.
"Unpleasant", "disloyal", "ungrateful" and "bad-mannered" were just a few of the choice terms she used to describe Fillon's statement.
"He (François Fillon) appears to be a little ungrateful vis-à-vis Nicolas Sarkozy who made him what he is today," she said.
"I don't think it's very chic (an attribute which is of course very important to Dati - in all senses of the word)," she continued.
"We tell our children to be well mannered and to get a good eduction. This is simply rude in relation to Nicolas Sarkozy. He's not dead is he?"
Of course this isn't the first time the two have locked political horns - so to speak.
Even though she has thrown in the towel after the UMP parachuted in Fillon to stand for a safe for Parisian seat (and one she coveted) in the upcoming National Assembly elections, Dati is clearly still smarting.
And this is a woman who, love her or loathe her, you just can't and probably shouldn't ignore.
There's denying that she knows how to make and impact - and not necessarily for the right reasons.
During her time as justice minister she came in from opposition criticism for her inability to handle her portfolio and the reports of her ministry haemorrhaging staff were seen as an indication of a woman who was difficult to work with.
Glossy magazines had a field day, regularly featuring photographs of an elegant and stylish Dati only too happy to pose for the camera and of course the weekly satirical magazine Le Canard enchaîné was unrelenting in lampooning her.
The polemic (good word that - the French love it) surrounding her return to work just days after giving birth to a baby whose paternity of course was the subject of endless speculation.
Even when she was fired - whoops sorry, left the government to take up her seat in the European parliament in 2009, she didn't quite disappear from the domestic political scene especially as she had been elected mayor of the seventh arrondissement of Paris in 2008,.
From apparent exile in Brussels and Strasbourg Dati has continued to make to make a splash, appearing on an M6 "fly on the wall" documentary in which she was less than complimentary about her new job.
She has popped up regularly on television - be it to explain the economics behind "fellation" or later throwing a "dildo" into a discussion on French secularism.
Both were bloopers of course, which she was able to smile about after the videos went viral and put down to the speed at which she speaks.
Always an ardent supporter of Nicolas Sarkozy, Dati was a brought back from duty in Brussels to accompany him during part of his campaigning, adding her own personal fashion statement late in the day by appearing on the early morning news magazine La Matinale on Canal + sporting a sweater with a design emblazoned on the back which to all the world (except Dati) looked to be that of a giant cannabis plant leaf.
In what is likely to become a struggle for control of the party (after the elections), Dati knows exactly how to position herself and make the most of her undoubted media-friendly talent - albeit sometimes to her cost.
Expect more fun and games to follow.