France and Germany have reached agreement to boost the eurozone's rescue fund to €2tn (£1.75tn) as part of a "comprehensive plan" to resolve the sovereign debt crisis, which this weekend's summit should endorse, EU diplomats said.

The growing confidence that a deal can be struck at this Sunday's crisis summit came amid signs of market pressure on France following the warning by the ratings agency Moody's that it might review the country's coveted AAA rating because of the cost of bailing out its banks and other members of the eurozone. The leaders of France and Germany hope to agree a deal that will assuage market uncertainties or, worse, volatility, in the run-up to the G20 summit in Cannes early next month.

France would now have to pay more than a percentage point – 114 basis points – over the price paid by Germany to borrow for 10 years as the gap between the two country's bond yields widened to their highest level since 1992.

The news cheered US investors. All the major stock markets surged, with the Dow Jones Industrial Average rising 250 points, or 2.2%, to 11,651, after earlier falling by 101 points earlier in the day.

US markets have previously reacted uneasily to any new news from Europe. Earlier in the day Goldman Sachs reported third-quarter losses of $393m, only its second loss in 12 years, and chief financial officer David Viniar said market volatility had contributed to the fall.

"Last week there was a big market rally; yesterday there was a big market decline," Viniar said.

Jack Ablin, chief investment officer of Harris Private Bank, said: "We are all reacting to headlines – every new headline triggers another move. There is so much uncertainty it's difficult to navigate."

Berlin had dampened down prospects of a full-scale deal, although EU diplomats close to the talks say the Franco-German agreement covers boosting the financial firewalls for eurozone members to withstand the threat of a "credit event" or sovereign debt default in weaker countries.

This takes two forms. First, the main bailout fund, the European financial stability facility, will be given additional levers enabling it to offer first-loss guarantees for bondholders, be they private or public. Senior diplomats say this will deliver a fivefold increase in the fund's firepower – giving it more than €2tn compared with the current €440bn lending capability. The EFSF will in effect become an insurer, thereby overcoming European Central Bank resistance to the idea of turning into a bank.

Second, Berlin and Paris have agreed that Europe's banks should be recapitalised to meet the 9% capital ratio that the European Banking Authority is demanding after its re-examination of the exposure levels of 60 to 70 "systemic" banks. The EBA has marked these exposures much closer to current market values.

It is said that the overall recapitalisation required will be closer to €100bn rather than the €200bn talked about by Christine Lagarde, IMF managing director, and others. French and German banks, senior sources said, can meet the new capital ratio target on their own without recourse to state funds, let alone the EFSF. Other countries' banks, however, may need financial support from the state or the EFSF.

Berlin and Paris are also said by those close to the negotiations to be edging nearer to agreeing on the increased scale of private sector involvement in the second rescue package (€109bn) for Greece. This was set at a voluntary 21% "haircut" in the July package but, under worsening overall economic conditions and a likely restructuring of Greek debt, Germany has been pushing for losses of up to 50%. France, backed by the ECB, has resisted the idea, while EU officials have clearly indicated that a range of 30 to 50% is being considered.

Josef Ackermann, Deutsche Bank's outgoing chief executive, held talks on Tuesday with senior EU officials on behalf of disgruntled bondholders. But there are signs that they are reluctantly accepting the need for bigger "haircuts" under the comprehensive plan to resolve the sovereign debt crisis. "We're not talking about a unilateral, one-sided restructuring of Greek debt," the diplomats said ahead of the imminent arrival of the full report from the troika of ECB, IMF and European commission on Greece's compliance with the bailout terms.

Senior EU officials admit that technical details remain to be settled. Some of these will be agreed by finance ministers who meet on Saturday, while others will await final agreement in the run-up to the G20 summit in Cannes. "It's a huge agenda," senior officials said of the plan of work for the summit. "But there will be a number of breakthroughs."

They added: "We thought the [Greek] package of 21 July was a big step, but obviously it was not enough and now we're pretty confident that markets will say that these people really mean what they say and will ensure stability."