Paris — At the same moment when Ronald Reagan went on American television to announce the dispatch of marines to Beirut, French President Francois Mitterrand was appearing on French screens with the same message.
Mr. Mitterrand announced that 1,100 French paratroopers and infantry would be deployed in the Lebanese capital, 350 of them arriving Sept. 23.
The coordination between the two presidents reflects their agreement over what to do to stop the violence in Lebanon. It also shows how the Mideast strategies of Paris and Washington have moved closer together following Mr. Reagan's recently unveiled peace plan and the massacre of Palestinians.
American diplomats expressed delight that the French were joining the peacekeeping force. ''We didn't want to go in alone,'' a US diplomat said. ''A multinational force has more stature, but of course we didn't want it to be so multinational as to include the Soviets.''
Unlike with the Soviets, the US and France are in complete agreement on strategy in Lebanon. Both Paris and Washington are demanding that the Israelis pull out of Beirut.
Beyond this pullback, the French want both the Israelis and the Syrians to withdraw from the country. Special US Middle East envoy Philip C. Habib met Sept. 21 with French Foreign Minister Claude Cheysson, and Mr. Cheysson later told reporters that both countries wanted all foreign forces evacuated from Lebanon.
''Without such an evacuation, Lebanon's integrity and sovereignty could not be possible,'' Mr. Cheysson said. ''We are 100 percent, I would say 200 percent, in agreement with the Americans on this point.''
It is only after foreign troops are removed from Lebanon that the French and the Americans disagree on how to make peace in the Mideast. Mr. Mitterrand believes that Israel must negotiate directly with the PLO and accede to the establishment of an independent Palestinian state.
But while the French President is insistent on this point, he has not rebuffed the recently unveiled Reagan plan which rules out such a state. ''President Reagan's proposals seem to aim in the direction we have been defending,'' he said.
For now, though, the first concern is Lebanon. The French are participating in the peacekeeping force not only out of humanitarian feelings, but because they have strong ties to Lebanon.
Since the 16th century, France has, to a greater or lesser extent, made itself the protector of Lebanon's large Christian population. In 1860 it sent a large peacekeeping force to the country after Muslims massacred thousands of Maronites.
After World War I, the French assumed a League of Nations protectorate for Lebanon. In 1941, they liberated the country, and in 1946, French troops finally withdrew.
But the ties remain. Many Frenchmen, as columnist Jean Dutourd put it in France Soir this week, remember Lebanon before its civil war as ''a delicious country, a little France of the Middle East.''
Historical and sentimental attachments aside, the French also want to remain active in the Mideast because much of its livelihood depends on the area. France receives much of its oil from the region and exports large amounts of high technology and arms there.
Remember above all, ''we're critically tied to the region,'' a French Foreign Ministry official said in explaining why his country was sending troops to Beirut.
Finally, France's new Socialist government has an ideological commitment to keeping Lebanon and other third-world countries from American or Soviet domination. ''We want to keep the region out of the East-West conflict,'' the Foreign Ministry official said.