Egyptian President Hosni Mubarak won a cautious endorsement of his Middle East peace initiative from France today during a stopover here en route to Washington for talks with President Reagan.

Speaking after a three-hour meeting between the Egyptian leader and French President Francois Mitterrand, a French spokesman said that Mubarak's proposals could "simplify" and "accelerate" the peace process in the Middle East. He added, however, that such an "energetic" initiative could run into opposition.

The statement marked the first official French comment on Mubarak's call for direct talks between the United States and a joint Jordanian-Palestinian delegation as a preliminary to international talks involving both Israel and the Palestine Liberation Organization.

As a European power with extensive interests in the Middle East and good relations with both Israel and the Arab countries, France sees itself as having a significant role to play in encouraging new talks on the Palestinian problem. French Foreign Minister Roland Dumas is due to visit Moscow next week for talks with Soviet officials on the latest peace moves after a meeting with PLO leader Yasser Arafat in Tunis.

Chatting with journalists at the Elysee presidential palace here after his meeting with Mitterrand, Mubarak said he had asked for French support in persuading President Reagan to accept his initiative. He described his mission to the United States as "a difficult operation," adding that had no guarantee that he would be able to "100 percent convince" the American president of the feasibility of his plans.

The official U.S. position, as expressed by Secretary of State George P. Shultz, is that it will not agree to talks with the Palestinians until the PLO formally recognizes the state of Israel. Mubarak has argued that a joint endorsement by Arafat and Jordan's King Hussein of all United Nations resolutions -- including Resolution 242 which recognizes Israel's right to live within secure and recognized frontiers -- amounts to implicit recognition of the Jewish state.