Even if Mr Ponsolle's deadline were met, the history of these banking crises suggests it would take at least until the end of the year to complete the negotiations over the company's pounds 8bn debts.
The real brinkmanship will come not in July but when the handful of top banks now attempting to settle with Eurotunnel try to persuade the rest of the 225-strong syndicate of lenders to agree.
Eurotunnel shareholders would do well to study the $7.6bn (pounds 4.9bn) rescue of Rupert Murdoch's News Corporation, where the top banks agreed among themselves within weeks, but the company nearly foundered because of squabbles with the smaller lenders.
On the night of 6 December, 1990, one small and obstreperous American bank, Pittsburgh National, almost bankrupted News Corp. Pittsburgh was owed just $10m, but told Mr Murdoch it wanted its money back - or else.
News Corp could not pay because that would have triggered demands from every one of the 146 lenders in its syndicates, which would have wrecked the refinancing plan and brought the whole company tumbling down into receivership.
The senior banker organising the rescue, quoted in William Shawcross's biography of Rupert Murdoch, said: "It's not a pretty sight to see a great man like that. He was so vulnerable. One phone call could mean the end of his whole life's work." Pittsburgh finally came back in line after a conversation with Mr Murdoch himself, two hours before the repayment deadline.
Although the companies are very different, the two rescues share one characteristic that is lurking in their loan agreements like a time bomb: they require approval from every single one of the banks in each syndicate before a financial restructuring can proceed.
This is a notoriously difficult problem. At a recent seminar on how to improve the co-ordination of international financial rescues, organised by the Bank of England, the 100 per cent vote was described by a director of one of Europe's largest banks as nothing more than a recipe for blackmail.
Whatever the merits of the rescue plan involved, and no matter how rosy the long-term future of the company, there are invariably groups of banks or single organisations that hold out for their own special reasons.
The seminar heard that sometimes their motives are perfectly valid, as when the lead banks steamroller smaller banks into accepting unfair terms that ignore conditions in their original loan agreements.
In other cases, the lenders that cause the problem are simply unaware of the worldwide repercussions of their demands for their money back and, like Pittsburgh, they doggedly stick to their rulebooks like small town bankers foreclosing on a domestic mortgage.
But more often banks, or groups of banks, hold back their agreement simply to extort special terms or to force other banks to buy them out, because they know the rescue cannot proceed without their agreement.
Modern financial engineering has made the situation still more complex, since loans are now traded in a secondary market for debt, so it is often hard to tell who the creditors really are. Companies in difficulty are increasingly having to deal with the bond markets as well, because that is where they have done a lot of their recent borrowing.
As a result of Mr Murdoch's cliff-hanging rescue, the Bank of England began a campaign to persuade companies to put majority rather than unanimous voting rules into their loan agreements, and it looked for a while as if the blackmail problem was receding.
Eurotunnel itself appreciated the difficulties well enough, so that when it was refinanced through a rights issue and new bank loans in 1994 the company no longer had to seek the 100 per cent approval of its banks. However, it was the decision last September to stop paying interest on the bulk of the debt that triggered clauses in the loan agreement and took the company back to square one, with a requirement for unanimity.
The fact is that a completely bust company is invariably going to need the approval of all its banks in order to survive, and in practice can only short circuit that problem if the big lenders agree to buy out the smaller ones, which is something they are rarely prepared to do.
Is this messy process really a sensible way of dealing with the rescue of an international company? What begins as an attempt to set up a life support machine usually ends up as a private squabble between bankers in which the interests of other creditors and shareholders take second place. The whole rescue package will inevitably be biased towards satisfying the most belligerent rather than the most public-spirited banks.
Even if the banks are right when they claim they are acting in the long- term interests of creditors, employees and shareholders, the secrecy surrounding the negotiations creates intense suspicions about what they are really up to.
Interestingly, the mixture of French financial culture and Anglo-Saxon banking attitudes during the negotiations over Eurotunnel may point to a way in which these problems can be overcome.
The procedure used for Eurotunnel, where Lord Wakeham and Robert Badinter were appointed in February as informal mediators by the French courts, has been drawing praise from bankers who until recently were intensely hostile to letting any outsiders interfere in their negotiations. Indeed, there was outrage when the idea of intervention by the French courts was first suggested, but that has now died away.
One advantage of mediation is that the banks benefit from outside help in dealing with Eurotunnel's stubborn board. The board's posturing over shareholders' rights has been laughable for a company that, two years ago, persuaded its shareholders to part with pounds 850m in a rights issue that has little prospect of financial viability unless at least half the pounds 8bn debt is written off.
Furthermore, any solution that has the stamp of approval of the mediators could also help the banks sell the deal to the awkward squads in their own lending syndicates.
Significantly, the Bank of England seminar, attended by representatives of some of the largest banks in the world, took on board the message about the need to introduce impartial outsiders. If there was a consensus, it was that the rescue process had to be distanced from the lead banks and squabbling syndicates to give it wider acceptability.
One proposal was that an independent chairman should be appointed to bank negotiating committees. Others suggested opening up the committees to a wider group of interests.
Almost everybody involved agreed that bank-led rescues are better than insolvency procedures such as receivership, which cost a fortune, take years to grind through the courts, and are less likely to preserve the businesses in difficulty. All that is needed is for the banks to make their methods fairer and more acceptable to everybody else involved.