It is a laudable ambition and a difficult one for this most Italian of French cities. Nizza la Bella has always been a problem child since it first came under Paris's rule in 1860.
Mr Estrosi, 37, a former professional motorcycle racer for the Pernod-Ricard team who still likes to move around town on two wheels, clad in leather, is the main conservative politician facing down the challenge in the city of Jean-Marie Le Pen, leader of the far right anti-immigration National Front. Both men are standing for Nice constituencies, although not in the same one, in the National Assembly elections starting on Sunday.
Mr Estrosi, first elected to parliament in 1988, said last weekend that he believed Mr Le Pen was heading for a first-round score of 25-27 per cent in the third Nice constituency, compared with a likely national average for the extreme right of 11-12 per cent. Mr Le Pen is likely to be defeated in the second, run-off round on 28 March. Opinion polls give Mr Estrosi, the combined candidate of the Gaullist RPR and centre-right Union for French Democracy (UDF), a comfortable victory in an expected conservative landslide.
Nice, for the rest of France, is a place of colourful casino wars, of gangland feuds, of big-time crime, the sort of crime where people just disappear, their feet in concrete, into the inappropriately named Baie des Anges, the Bay of Angels, Locally, however, the big-time stuff, which has in any case died down in recent years, is almost irrelevant, a phenomenon which affects only the big-timers. For all other natives, it's the small-time crime that is the worry.
It is a city used to having a strong father in control. The last was Mayor Jacques Medecin, who fled nearly three years ago to avoid facing tax-fraud charges.
The Medecins - Jacques and his father Jean before him - had run the city for nearly half of its time as a French city, since December 1928.
Jacques Medecin changed parties twice during his tenure, moving from the UDF, in which he had a brief spell as tourism minister in the 1970s, to the RPR and then to the more right- wing and tiny Centre National des Independants. His constant threat was to make the unpardonable leap to the National Front.
In regional elections last year, in a recorded message to his townspeople, Mr Medecin, supervising the construction of his new villa in Punta del Este, urged them to vote for Mr Le Pen. This year, he has just told them to support the leading candidates of the right. Mr Estrosi, a native Nicois, believes Mr Le Pen, a Breton, stands a chance of being ahead in the first round but has made it his personal crusade to ensure he does not.
'I don't just want to beat the National Front,' he said said. 'I want to get rid of the danger for ever by taking the biggest score possible.'
Mr Estrosi resorts to tough words on immigration, referring to 'rampant Maghrebinisation', or saying that he would sooner renovate run- down districts to make way for new university buildings and 'academics and students than immigrants'.
It is a discourse which worries many in the more centrist UDF.
'Estrosi is young,' said an embarrassed UDF official in the neighbouring Var department, hearing of the remarks.
Mr Estrosi's direct battle is against a local Nicois National Front member, Jacques Peyrat, a lawyer and a popular town councillor. The National Assembly election is seen locally as a dress-rehearsal for two men likely to run for mayor in the next municipal elections.
The city hall vote is not due for another two years but there is talk of bringing it forward in order to settle Mr Medecin's succession once and for all. His place was taken by Honore Bailet, who so far has failed to make an impact. Now, Mr Bailet's image is sullied by the fact that a member of his family has been charged in a murder case.
At the moment, Mr Peyrat looks as strong a mayoral candidate as Mr Estrosi. The Gaullist argues that a National Front mayor would just compound Nice's isolation, driving away visitors and investors.
A regular theme in Nice conversation is the vacuum caused by the departure of Mr Medecin. To the outsider, the fact that he is missed is difficult to understand.
'Why do people miss him?' asked a young Provencal. 'Because of insecurity. He had a good municipal police force. There are thugs all over the place now and you just don't feel safe any more. And we've got the Mafia coming in.'
In January, 11 bombs exploded in Nice. The devices, often made of different materials, hit small shops, lawyers' offices and cafes. There was no apparent pattern. This month, police rounded up 15 suspects. There has been talk of extreme-right involvement. Most locals, however, put it down to a Mafia extortion racket. Mr Estrosi tells election meetings of the conservatives' plan to create a 'National Guard' from national servicemen, an extra police force to bolster security throughout France. 'We are sending soldiers to chase after looters in Somalia.' he said. 'You think there are no looters on the streets of France?'
ON SUNDAY, France votes in the first of two rounds for the 577 seats of the National Assembly, the lower house of parliament from which the government is traditionally formed. In those constituencies, probably no more than 80 to 100, where a candidate gains 50 per cent or more of the vote in the first round, he or she is automatically elected and there is no second-round vote.
On 28 March, in all other constituencies, candidates who obtained 12.5 per cent or more of the vote are entitled to stand. Usually, local between-round deals ensure no more than two candidates go forward but the far-right National Front and the ecologists have said they will not respect this convention.
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