Today's parliamentary elections in France were preceded by an intensive advertising campaign aimed at persuading the 37 million registered voters to accept a dramatic change in procedures.

A catchy slogan -- un seul jour, un seul tour (only one day, only one round) -- was coined to remind voters to give up their old habits. Under the previous system, which France has used to elect the National Assembly since 1958, electors were asked to vote twice. The first round was a kind of popularity contest while the second, held a week later, involved a runoff between the leading candidates.

Today's election was held under a complex system of proportional representation introduced last year at President Francois Mitterrand's insistence in what was widely viewed as an attempt to reduce the scale of the likely right-wing victory. By distributing the 577 seats in the assembly more evenly, the new system effectively prevented any one political party from winning an overall majority, as the Socialists did in 1981.

Accustomed to voting directly for individual candidates, the electors today were asked to choose between long lists of candidates drawn up by rival political parties. The old single-seat constituencies were replaced by multiple-seat constituencies.

In Paris, where a total of 21 assembly seats were at stake, voters were given a choice betweeen 15 different lists of candidates, ranging from established parties like the Socialists and neo-Gaullists to such fringe groups as the Planetary Unity Party and the Ecology and Humanism Party. Seats were only distributed to parties receiving more than 5 percent of the total vote in a department.

By preventing voters from expressing a preference for individual candidates, the list system removed much of the traditional suspense from election night.

Using procedures similar to those employed under the Fourth Republic, 1946-58, the distribution of seats this time was weighted in favor of the larger parties. The system, which used the formula of the "highest average," is illustrated by the example of the Puy-de-Dome constituency in central France, where former president Valery Giscard d'Estaing was running at the head of a joint opposition ticket.

Eight parties were contesting 20 seats. Four lists of fringe parties, such as the Greens and the extreme left, were eliminated because they did not achieve 5 percent of the vote. Giscard's UDF-RPR list received 141,205 votes, the Socialists 106,993 votes, Communists 23,583 and National Front 17,081.

Seats were distributed according to a quotient, which was reached by dividing the total number of votes for the four parties by the number of seats. In this case, the quotient was 14,443 votes.

Each list was then awarded one seat for every 14,443 votes. The UDF-RPR won nine seats, the Socialists seven, and the Communists and National Front one each, leaving two seats still to be distributed. These seats were then distributed by the "highest average," which was obtained by dividing the votes of each list by the number of seats already awarded, plus one. Hence:

UDF-RPR: 141,205 divided by 10 (9 seats plus 1) = 14,120.

Socialists: 106,993 divided by 8 (7 seats plus 1) = 13,374.

Communists: 23,583 divided by 2 (1 seat plus 1) = 11,791.

National Front: 17,081 divided by 2 (1 seat plus 1) = 8,540.

The two seats went to Giscard's list and the Socialists, with the "highest average." UDF-RPR won 10 seats, Socialists 8, and the Communists and National Front 1 each.