There is a role wandering around in search of a hero," Egypt's Gamal Abdel Nasser once wrote of the Middle East, and promptly cast himself in it. As it turned out, his successor, Anwar Sadat, did as much as anybody in the Middle East to fill the role. With Sadat gone, there are no heroic figures in sight.

But to the extent that there may be a "role wandering around" in search of a mediator with a fresh eye and a minimum of political encumbrances, a likely candidate could be French President Francois Mitterrand. How things look depends to some extent on where you are. But from here, anyway, the Arab-Israeli conflict takes on a new and different look, if only because the Mitterrand government has a distinctly new and different approach.

It is new in the sense that Mitterrand has a Socialist Party connection with Israel's Labor Party and, with that, a special sensitivity for Israel's security that his predecessor, Val,ery Giscard d'Estaing, never quite managed to convey.

And it differs measurably from Europe's collective Middle East "initiative," in that it does not come across competitively as an either/or alternative to the slow-moving (some say moribund) Camp David "autonomy" formula for resolving the Palestinian issue on the West Bank and Gaza Strip.

It's a subtle difference, and the French still care deeply about their commercial interests (oil and trade) in the Arab world. But the 10 members of the European Commission, which launched Europe into the thick of the Middle East peace-making process, managed to give the impression that this was all they cared about.

The French are being careful to avoid slamming doors ("Camp David is dead," the British and other Europeans are fond of saying). The French line is that Camp David, while it can never be the whole answer, is the only door open now. Similarly, the French have not rushed to embrace the eight- point peace plan put forward by Saudi Arabia's Crown Prince Fahd, even while they believe that it has elements worth pursuing in due course.

One result, already detectable, is, if not a meeting of minds, at least a far greater mutual understanding between France and the United States on the Middle East. Says an American diplomat here: "Mitterrand is much more responsible on the Middle East; Giscard played the Arab side."

A French counterpart sees his president as "closer to Camp David" as a consequence of his Yorktown talks with Ronald Reagan and "Reagan more open-minded on the Fahd plan."

In short, the Mitterrand "grand design for French policy" in the Middle East, described to me by well-placed policy makers, rests firmly on the need to win the confidence of Israel, as well as the United States--even while maintaining critically important commercial and political relations with the Arabs. This means trying to direct the European Commission's intervention in a way that would give it more influence on both sides of the conflict.

Hence the largely underestimated French hand in trying to arrange for European contingents in the international force that is supposed to help keep the peace once Israel withdraws from the Sinai as the final step in the Egyptian-Israeli peace treaty.

As one French diplomat tells it, Sadat waited for the outcome of last May's French election to approach Mitterrand, as well as other Europeans. The British were reportedly reluctant; Mitterrand took the lead. The Italians have volunteered and a final decision awaits only the approval of the "10."

"For the first time," says one Middle East expert here, "the Europeans would have some real credibility if they were actively engaged in policing Israel's security."

Mitterrand is now planning a visit to Israel in January, to press his mediator's role. Interestingly, he was to go right after his election. When the Israelis bombed the French-built nuclear reactor in Baghdad, he went instead to Saudi Arabia. An aide describes the sequence by way of illustrating "even- handedness," Mitterrand-style.

The Mitterrand government's Middle East policy makers insist they have no fixed prejudgments on Camp David's fate. But they do have in hand a scenario, if "autonomy" languishes. Egypt's new president, Hosni Mubarak, they figure, may let it die, blame Israel, and start working Egypt's way back into the Arab mainstream.

At that point, Mitterrand intends to be ready, as one official puts it, "to help build a bridge between Camp David and the Fahd plan."

All this presupposes some way of bringing Israel's Menachem Begin along, on which score the French offer no assurances. What does seem assured, from talking to Mitterrand's men, is that as the search continues for a Middle East solution, the French intend to play a substantial (if not quite heroic) role.