At least for one of the candidates still left in the race, Jean-Francois Copé, the party's current secretary general.
If he runs out the winner against former prime minister François Fillon in November, the chances are the UMP will be able to drop any pretence of being a centre-right one.
The signs are there.
First up there's his aptly entitled "Manifesto pour une droite décomplexée", extracts of which you can read in Le Figaro and which illustrate how Copé believes there's an "anti-white discrimination" in some areas of France.
And presumably that so-called discrimination can be found, if you follow Copé's line of thinking, in the very same areas as the ones quoted in a campaign speech he gave last Friday in the southeastern town of Draguignan.
Jean--François Copé in Draguignan (screenshot from i>Télé report)
Apart from banging on about the current government's mishandling of the country which is, after all, what a party in opposition is supposed to do, Copé also revealed a little more of what we might expect from the UMP with him at the head.
You see, apparently he can "understand the exasperation of some people who return home from work in the evening to learn that their son has had his pain au chocolate taken from him, just as he was leaving school, by thugs who explained to him that Ramadan means fasting."
Take a listen to the clip.
Right. Yes definitely an "uninhibited Right" and not a direction some other leading UMP figures would share, as former finance minister François Baroin was clear to point out at the weekend.
Quite apart from the offensive and inflammatory nature of Copé's remark with its obvious undertones which surely don't need to be spellt out (but have been nonetheless by many over the past couple of days in what the French almost lovingly refer to as a "polemic") there's also an essential problem with his little anecdote.
When was the example quoted by Copé as leading to his enlightened understanding of some parents' annoyance supposed to have taken place exactly?
2012? Impossible as many have since pointed out because Ramadan fell during the school holidays
2011? Equally unfeasible for exactly the same reason.
So that leaves the most recent possible date for such a act 2010
So in other words, poor old Copé has been waiting two whole years to bring the plight of that child to the public's attention and to show just how in tune he is with the thinking of M. et Madame Average French citizen?
Yes M. Copé, let the French eat their pain au chocolat.