Will France and Britain choose the 'chunnel' or the 'brunnel'?

Napoleon Bonaparte first suggested the idea more than 180 years ago. Since then his countrymen have attempted twice without success to realize it. Despite that long, sad history, Margaret Thatcher and Francois Mitterrand want to try once again to connect Britain and France by building a tunnel under the English Channel.

At the end of a Franco-British summit here Friday, the British prime minister and the French President issued a special joint declaration recognizing ''the potential importance of a cross-channel fixed link'' and asserting that the project ''would be technically feasible and financially viable.''

The two leaders ordered a study group to report in less than three months, and French Transport Ministry officials say that a choice of projects could be made by the end of next year, with work beginning sometime in 1986.

What makes this tunnel timetable seem more serious than past ones is British determination. French officials say Mrs. Thatcher has raised the subject numerous times with Mr. Mitterrand, and she seems willing to give the needed political guarantees to begin construction.

''It's a real change in the British attitude,'' says Max Roche of the French Transport Ministry. ''In the past, the British have always been hesitant.''

That is an understatement. Both previous attempts to dig across the English Channel were canceled by London either because of financial worries or fear of tying the island-nation too close to the Continent.

The first tunnel, begun in 1880 from the white cliffs of Dover, was called off after British alarmists raised the possibility of invading French troops suddenly turning up at London's Victoria Station dressed as nuns on holiday.

The second attempt to construct a tunnel came in 1974. More than 1,000 feet of new tunnel were drilled before a Labour government came to power in London and decided that the cost was too high.

When Mrs. Thatcher became prime minister in 1979, she continued tradition and opposed French plans to revive the project. Instead of public funding, the customary way of building most large tunnel or bridge projects, she insisted on private financing. The French refused.

Meanwhile, the need for a channel link was becoming more and more apparent. More than 20 million people now cross the channel each year, compared to 5.5 million in 1962, and freight haulage has increased by more than five times in the past decade. Both figures are expected to continue increasing rapidly.

Sensing a profit, business on both sides of the channel began putting forth new proposals. This time, the French agreed on private financing. And the British gave a promise not to pull out if the project was started.

The next step is to choose among competing projects. From the seven proposals originally put forth, two real candidates remain.

One would be a double-tube rail tunnel shuttling vehicles on wagons. It is dubbed the ''chunnel.'' The other would be a combined bridge-tunnel. It would start out as a bridge on each coast before diving under the busy channel shipping lanes. It is dubbed the ''brunnel.''

The big advantage of the ''brunnel'' is that it would permit automobiles to drive across. But the cost would be much higher than the simpler ''chunnel'' train link, at least 50 billion francs ($5.5 billion) compared to some 20 billion francs ($2.2 billion), according to the French Transport Ministry.

Moreover, the technology needed for the bridge-tunnel combination has never been tested. Mr. Roche of the Transport Ministry estimates that some 200 million francs ($22.2 million) of studies would be needed before construction could begin.

''Bet on the tunnel,'' he advises.

Despite the renewed will on both sides, there has been no agreement on what should be done if the project hits an unforeseen snag during construction.

The banks proposing to finance the operation insist on public guarantees. The French agree. The British, of course, refuse. And cynics' eyebrows rise.

''I think this time we'll finally build it,'' says Roche. ''But as long as there is no treaty signed, ratified by both parliaments, it's all reversible.''