We shall need to know two things about the outcome of the French presidential election rather than one. Who has won, and a further question – what do financial markets think of the result? The French know that there is this second judgement to come and many resent it. It arises because, as Nicolas Sarkozy's Prime Minister, François Fillon, said recently, "if the left puts the European treaty in doubt on the day after François Hollande is elected, at that point speculation against the euro would take off again, except that this time there would be nobody to prevent it".

Of course Mr Fillon was trying to frighten French voters into supporting the outgoing President, but his warning was not fanciful. For Mr Hollande has said clearly that he would wish to renegotiate the eurozone treaty so that it favours growth. He is likewise reluctant to entrench a so-called "golden rule" that would forbid budget deficits rising above the equivalent of 0.5 per cent of national output.

It is not that Mr Hollande's wishes are unreasonable, but the treaty as it stands is the only means available to the eurozone to compel budget rigour in Greece, Italy, Portugal, Spain and the rest. And, in turn, the treaty provides the financial markets with some comfort. But if France, of all countries, were to seek to unpick it, that would substantially reduce confidence in the common currency. Mr Hollande understands all this. In his speech launching his campaign, he referred to his true adversary. "My true adversary does not have a name, a face or a party. He never puts forward his candidacy, but nevertheless he governs." He went on: "My true adversary is the world of finance."

What is this world of finance to which Mr Hollande refers? It is France's creditors. They are numerous, for France has not had a balanced budget since 1974. And these creditors are the banks, insurance companies, pension funds and ordinary savers who own French government debt. Many of them are French institutions and French citizens; others sit in London or in New York or in smaller financial markets. You can call them bondholders. For the moment, they are more powerful than any individual national government, perhaps even stronger than the 17 member of the eurozone combined.

In the French mind, this enemy has many aliases. It could equally well be called the "Anglo-Saxons", the City and Wall Street. The hard left candidate, Jean-Luc Mélenchon, often takes up this theme. In the latest polls, he has 14.5 per cent of the intentions to vote and lies third after Mr Sarkozy and Mr Hollande who are tied on 27 per cent. The other day, this cultivated man, speaking at the Bastille in Paris, broke into English to observe: "Yes, there are thousands of red flags at the Bastille again... Yes, we are very dangerous." And then, returning to his native language, rather than criticising, say, the City, as one would expect, he turned his guns on the English language itself. "We speak fluently "globish"... the language of the occupier – the occupier of our minds," he remarked. "Our battle is a cultural battle," he added, calling French the "language of the heart" and English the language of "accounting".

Another contender, Jacques Cheminade, with an almost invisible share of voting intentions, puts this proclamation on his election posters: "Un monde sans la City ni Wall Street" – a world without the City or Wall Street. But as he thinks the Beatles were invented by what he calls the British propaganda services and that the Queen runs the international drug trade, we need not take his view too seriously. On the other hand, the French philosopher Jean-Pierre Dupuy, who teaches at Stanford University in the US, said he was ashamed to see that in France "politics lets itself be humiliated by the economy". "Politics is on its knees when confronting economic matters and the markets," he said recently.

Another consequence of the requirement to satisfy France's creditors is that mainstream candidates put forward similar economic policies. Thus Mr Sarkozy is planning to reach equilibrium in the government's finances by 2016, while Mr Hollande is aiming at 2017. To achieve this, Mr Sarkozy relies more upon cuts in public spending and less on tax rises. Neither side give much detail.

Nonetheless, Mr Hollande, with his talk of renegotiation, has given Mr Sarkozy the opening he needs. He has repeatedly raised the spectre of France sinking into the same debt crises as Spain and Greece if he loses power. He refers to countries that become incapable of meeting their promises to creditors, and as a consequence having to reduce pensions and cut wages. What "our Spanish friends" and "our Greek friends" are experiencing, he urges, should act as a wake-up call. If François Hollande wins, he added, "you will have Greece or you will have Spain".

This is hardball politics, French-style. I would have thought it would be pretty effective, but in fact Mr Hollande's support has remained stable and he appears to be on the way to a convincing win in the second round on 6 May. Mr Sarkozy is suffering from that most deadly of charges – he would say that, wouldn't he? Nonetheless, he could be right about the answer to the second question. The financial markets won't like Mr Hollande at the Élysée Palace.

a.whittamsmith@independent.co.uk