By Tony Connelly, Europe Editor, in Paris

And so another European leader has fallen into the eurozone debt crisis vortex.

Gone is Nicolas Sarkozy, only the second ever incumbent to be kicked out by the French after one term. In his place is Francois Hollande, a politician who, despite his storied affability and modesty, is presenting himself as the man to turn Europe – perhaps even the world – away from the path of austerity.

On Sunday I spoke to numerous supporters of Francois Hollande, both outside the Partie Socialiste’s headquarters on Rue de Solferino on the Left Bank, but also at the huge, boisterous celebrations on Place de la Bastille.

There was plenty of emotion – this was the first time the Left had got its hands on the Elysee Palace in 17 years – but also realism. One young man said this was a symbolic victory, but he didn’t think Hollande would have much room for manoeuvre because of the debt crisis.

Another declared confidently that the people who were celebrating would be back on the streets in six months because their new hero would be forced into line by the dictats of EU-led austerity.

One girl said she hoped – somewhat touchingly – that German chancellor Angela Merkel would afford the ideas of Francois Hollande the same attention as those of Nicolas Sarkozy.

What can Francois Hollande do?

During his campaign he promised an alternative to austerity, but not the moon and the stars. He wants 60,000 new teachers, but without any net increase in the levels of public sector employment.

He has promised to lower the retirement age back to 60 from 62, but only for those who started work at 18.

He pledged to tax those earning over €1 million at 75pc, but this is expected to have quite a few loopholes and is not expected to bring in that much money.

And, of course, he has promised to renegotiate the fiscal treaty.

The new president-elect has been creatively ambiguous about what he means. He has said he won’t ratify the treaty as it is, but in terms of specifics he has only spoken of what he would add, not what he would take out.

Full-scale renegotiation of a text which has been signed by 25 sovereign governments would require everyone going back to the drawing board. Angela Merkel will not wear that, nor would many other governments.

What would a new President Hollande add?

He has mentioned four things: he wants new EU bonds to fund large-scale transport and technology infrastructure projects (these are sometimes referred to as project bonds). He wants more money in the European Investment Bank (EIB). He wants a Financial Transactions Tax (FTT) the proceeds of which would go towards job growth. And he would like unspent EU structural funds to be used to leverage further infrastructure spending.

The European Commissioner for Economic Affairs Olli Rehn has acknowledged some of these ideas, especially the EIB leveraging. Indeed he’s spoken about governments contributing an extra €10 billion to the EIB which could leverage a total spend of €60 billion.

When you break these ideas down, though, there are problems.

The EIB is a notoriously risk-averse entity. It would need private investment alongside whatever governments put in. And there’s no guarantee that cash starved governments will cough up.

Boosting structural funds also sounds like a good idea, but remember we are about to engage in highly toxic negotiations for the next round of the European Union budget which will run from 2014 to 2020. Already Britain has been rattling cages over big cuts in expenditure, including over structural funds.

And a Financial Transaction Tax is something the Irish government and others, notably the UK, have been dead set against. When Francois Hollande demands something like that he knows it has to be done the hard way: through the normal EU negotiating process, where countries wield a veto.

None other than the UK Independence Party leader Nigel Farage MEP has already been out of the traps warning that Francois Hollande in the Elysee would be dangerous for Ireland, because of the FTT and the old chestnut of the corporate tax rate (one of Franois Hollande’s trusted MEPs, Pervenche Beres has already told RTE News that Ireland’s corporate tax rate was regarded as social dumping by the left).

So where does that leave the Irish government?

Interestingly, after Pervenche Beres made those comments in an interview I conducted with her and which ran on RTE’s This Week programme, Tanaiste Eamon Gilmore’s office was, I understand, anxious to make contact with her.

Eamon Gilmore was, indeed, invited to Rue Solferino to join the celebrations on Sunday. Was he also keen that elements of the Socialist Party needed to be kept “on message?”

It’s understood that there have been contacts ongoing in any event from the Tanaiste’s office to the Socialist camp – they are, after all, part of the same political family, the PES (Party of European Socialists).

In an interview with RTE just an hour after Francois Hollande’s victory Eamon Gilmore said he was assured that he did not intend to reopen the text of the fiscal treaty, but to add a growth agenda, the basis of which would be what I mentioned above.

The idea of a growth agenda was something the government had been pushing for a long time, he said. But he also acknowledged that there would be elements of Francois Hollande’s programme which the government did not agree with, such as the FTT and any further moves on Ireland’s corporate tax rate.

The Irish government will be anxious that the incoming president spells out more clearly what he intends to do with the fiscal treaty. Any lingering ambiguity will not help the government’s campaign for a Yes vote on May 31.

Francois Hollande will find out very quickly how constrained his programme might be by the financial markets and other European governments. He will be inaugurated probably around May 15 and there is talk of a trip to Berlin the very same day.

He will then travel to the G8 summit in Camp David on May 18, followed by a Nato Summit in Chicago the following week.

Then he will travel to Brussels for an informal summit of EU leaders. The Taoiseach Enda Kenny will no doubt look to grip Mr Hollande’s elbow – but so will every one else.