In France's 1995 presidential election, PM Edouard Balladur lost the right's runoff slot to Jacques Chirac by 700,000 votes, or just under 3%. Balladur had led in the polls until Chirac started criticizing Balladur for being outside the centrist political consensus, which was undoubtedly true. Let's say that Balladur keeps things less specific and ekes out a victory over Chirac in the first round. If he defeats Jospin in the second round, what would his presidency look like? Undoubtedly there will be major controversy, labor unrest and tanking poll numbers as happened in 1995 IOTL. Except here there would likely be no U-turn. The PS will be completely obstructionist and even parts of the right will be uneasy. How much can he get through? Let's say because of his age he doesn't run again in 2002, though probably his numbers will have improved during the latter half of his term. Does Balladur quit the RPR and try to form a party of likeminded politicians called the Parti Libéral, or go what I suspect is a fruitless route of forcibly converting the UDR to his economic ideology?
I'm afraid you make a big mistake here.
Balladur is NOT Thatcherian, and, for that matter, there is no French equivalent to Thatcher. No, sorry, there's Alain Madelin, who made a tremendous 3% in the 2002 elections, and a bunch of angry seniors, vocal teens and heavily state-funded business owners. And maybe Le Pen, at least when his electorate wasn't made with many dissatisfied workers. Actually, I think that Le Pen would be the best candidate for your Thatcherite scenario. After all, if you forget the antisemitism and racism, he's as civil as Gen. Pinochet.
Balladur was the candidate of the moderate, conservative circles, but more in the lines of Continental conservatism, whereas Chirac came back to the old Bonapartist, populist (in the american sense) roots of Gaullism. I would say that a Balladur Presidency would look like an early, more "bourgeois" version of the Sarkozy presidency : few reforms, or half-assed, or aimed at supporting electoral supports and not at modernising the country ; a more American-friendly foreign policy, and probably a social conservative stance.
A party called "Parti Libéral" in France ? It's basically the same as calling it the "Throw rocks on us please Party". No, he would probably have gone with something along the lines of the UMP.