LONDON -- Having sold France and England on the idea of building a rail line under the English Channel, promoters of the proposed tunnel must now start digging in the world's financial markets for the $9.5 billion they'll need to pay for it.

Eurotunnel, an Anglo-French consortium of 15 banks and construction companies, is facing the task of persuading banks and investors in the United States, Japan and Europe to back construction of the 31-mile double tunnel under the channel.

With tentative bank commitments hinging on one-sixth of the cost being raised in equity, the big test will come this fall when Eurotunnel attempts to sell $1.2 billion in stock.

Analysts consider the tunnel, billed as the world's biggest construction effort, to be a high-risk venture. A $325 million private placement last fall almost fell through when British and American institutions balked at the risk, and the consortium's members -- who had initially put up $75 million -- reportedly were forced to contribute more to complete the placement.

"That offering was poorly presented," said Alastair Morton, cochairman of Eurotunnel. "This time we will have a better story to tell and we will tell it better." In the next few weeks, Eurotunnel officials will make presentations to banks and institutions in New York, Toronto, Tokyo and 11 European cities.

Morton, the former chairman of the British merchant bank Guinness Peat, was hired by Eurotunnel last February to boost investor confidence in the project and to secure financing to enable construction to begin by December.

The tunnel, due to open in 1993, would allow high-speed trains to carry passengers between London and Paris in less than three hours. Passenger cars would be whisked across the channel in 35 minutes by shuttle trains.

Eurotunnel's plan was selected in January 1986 over three competing concepts for a fixed link across the channel. A treaty authorizing the privately funded venture was signed by France and England on July 29.

To realize the two-century-old dream of connecting the two nations, Morton, 49, has to persuade the investors that Eurotunnel can be built on budget and that enough people will use it over the next 50 years to make their investment pay off.

The project is budgeted at $9.5 billion -- $7.9 billion for construction, inflation and financing, and $1.6 billion in contingency funds for cost overruns. Raising that sum will hinge on the $1.2 billion stock offering, which is likely to take place in mid-November. A consortium of 50 international banks, including Citibank and Security Pacific, has agreed to lend $7.9 billion once Eurotunnel raises the remainder in equity.

About 80 percent of this fall's offering will be split between Paris and London. Morton said the remainder will be placed "with sophisticated investors" in the United States, Japan and elsewhere.

Eurotunnel officials and bankers involved with the public offering acknowledge the difficulty of the task.

"This is a more difficult challenge because it's an unusual offering," said Emmanuel Vasseur, senior vice president of Banque Indosuez, which is comanaging the stock offer in France. "It's a different animal from privatizations or anything else."

"This is not a company that makes widgets," added a banker with S.G. Warburg, which is leading the offer in Britain. "The key to selling these shares is explaining what this company will do."

An advertising campaign in France and England to explain the project and drum up investor interest is to begin in mid-September. Eurotunnel backers are less optimistic about winning support from U.S. investors, who largely turned down the chance to participate in last fall's private placement.

"It's too far away for the states," said Vasseur. "American investors are unwilling to take a political risk, but now we have taken a major step with ratification of a tunnel treaty," he said.

But many in the investment community are not convinced. A recent Sunday Times survey of London's top 50 institutional investors found only 12 percent willing to buy shares in Eurotunnel.

"The risk-reward ratio doesn't look attractive enough," said a spokesman for M & G Securities Ltd., a major London mutual fund manager. "The downside risks are just too great."

Richard Hannah, a transportation industry analyst with the Phillips & Drew brokerage in London, said the issue should be viewed as a venture capital operation because the project is based on economic assumptions and traffic projections made 50 years ahead, a time frame he considers too great to estimate with any accuracy.

"It comes down to an act of faith," Hannah said. "You've got to believe the projections are right."

Eurotunnel hopes to handle 30 million passenger crossings in its first year, about half of the total cross-channel passenger traffic. It projects crossings to almost triple by 2013.

The biggest risk, Hannah said, is that construction costs could balloon and eat up investors' equity. He noted that the Thames Barrier, a British flood-control project, ran 20 times over budget by the time it was completed in the late 1970s.

But Morton said the construction contract calls for the contractor to absorb 30 percent of overruns. Vasseur added that in the case of substantial overruns, the dividends projected in the first few years could be affected, "but that doesn't mean the equity will be wiped out."

Marketing of the equity issue, officials say, will focus on the potential for significant capital gains as the tunnel nears completion and robust dividends once the tunnel is open for business.

The project received a big boost last month when the French and British national railroads agreed on a plan to use France's high-speed TGV trains on Paris-London runs. The train would run at about 180 m.p.h. in France, slow to 100 m.p.h. for the crossing, and decrease to about 90 m.p.h. for the remainder of the trip. Morton said he was optimistic that by the year 2000 approval would be given for new tracks in Britain, allowing the train to reach higher speeds and reduce the trip to about 2 1/2 hours