At a simple white cross, one among the 9,386 at the Normandy American Military Cemetery, Nancy Reagan today left a bouquet of flowers on the anniversary of one of history's most famous invasions--June 6, 1944, D-Day.

"As I flew over the peaceful Normandy countryside, it was hard to imagine that 38 years ago there was not calm, but violence," she said, standing beneath a brooding gray sky and soft rain, her voice breaking. "Sadly, many of those who fought soon found calm in the rows of crosses and Stars of David that stretch before us. Today we honor those whose sacrifice is as lasting as the stone of this memorial."

Rising behind her was the 22-foot bronze statue "The Spirit of American Youth Rising From the Waves." It is set in a semicircular stone colonnade on the cliff above Omaha Beach and carved in it is an inscription: "This embattled shore, portal of freedom, is forever hallowed by the ideals, the valor and the sacrifices of our fellow countrymen."

"If my husband were here today, he would tell you how deeply he feels the responsibility of peace and freedom," she said. "He would tell you how we can best ensure that other young men on other beaches and other fields will not have to die. I think he would tell you of his ideas for nuclear peace. Certainly he would speak of Normandy's message to all who love liberty."

In remarks taped at the White House on May 31 and released to French television on Saturday, President Reagan told of the bitter battle that began the night of June 5, when "2,000 planes took off from English fields to drop soldiers by parachute behind enemy lines. By the early hours of June 6, the massive Allied armata, 5,000 ships, had begun to move across the cold and choppy water of the English Channel: D-day had begun.

"The code names 'Omaha,' 'Utah,' 'Gold,' 'Juno' and 'Sword' are now indelibly etched in history by the blood spilled on that 100-mile stretch of beach. More than 150,000 troops stormed Normandy that day, and by dusk they had established beachheads at each of the five invasion points. The toll was high. More than 10,500 of our young men were either dead, wounded or missing," the president said.

"Today, endless rows of simple white crosses mark their seacoast graves. The rusty helmets still buried in the sand and the ships and tanks still lying off the shore are testaments to their sacrifices," he said.

Today, from the memorial, Nancy Reagan walked to an overlook where she could see a portion of the four-mile-long Omaha Beach. Just recently, authorities found unexploded hand grenades in the sand, according to a White House aide. It is the spot where a beachhead eventually was established after bitter fighting. German artillery knocked out 16 of 19 bulldozers coming ashore, 27 of 32 landing crafts and a total of 2,000 American men were killed in this landing of the first infantry division here at Omaha Beach that June morning.

With Mrs. Reagan were Gen. John W. Donaldson, director of U.S. Battle Monuments Commission for France, and Gen. Christian Patte, U.S. Embassy defense attache in Paris. Then, accompanied by Antoinette de Beranger, curator of the D-Day museum in nearby Arromanches, she strolled through the wet grass along the cliff's edge.

The two women stood quietly, as de Beranger described the battle that took place. Before they parted, Mrs. Reagan leaned over and kissed the French woman on the cheek. Then they turned in the direction of the white crosses that cover nearly 172 acres here.

Walking down the paths to place flowers at the gravesite of American Red Cross volunteer Elizabeth Richardson, one of only four women buried at the cemetery, Mrs. Reagan passed markers bearing such names as Delmar C. McElmaney, Pvt., 507 Prcht. Inf. Rgt. California, June 6, 1944; Clifton M. Duke, Pvt., 119 Inf. 30 Div. Virginia, July 26, 1944; and Oliver A. Rahey, Pvt. 120 Inf. 30 Div., District of Columbia, Aug. 22, 1944.

There are 33 pairs of brothers buried side-by-side, as well as a father and son. One pair of brothers are Quintin and Theodore Roosevelt Jr., sons of the 26th president. Quintin died in World War I and until 1955 was buried at Chateau Thierry, when he was moved to Normandy to be buried with his brother, who died of a heart attack soon after coming ashore at Utah Beach on D-day.

Donaldson said later the cemetery represents 40 percent of those killed in the area in the weeks following the invasion. The rest were taken home for burial at the request of their families.

Later, Mrs. Reagan was the guest of honor at a luncheon given by the mayor of nearby Vierville-sur-Mer, Michel Hardelay, and his wife. The Hardelay house was one of seven left standing after the invasion and one of only two that still had its roof.

The house--about 50 yards from the beach--had been occupied by Germans and on the first day of the invasion Americans took it over. They used the front yard as a medical unit and the second floor balcony to direct the rest of the landing. Mayor Hardelay returned home six days after the landing, just as American Lt. R.M.A. Hirst was drilling holes into the foundation and getting ready to plant dynamite there. Hardelay persuaded him not to blow up the house and the two men have been friends ever since. Hirst now lives in Germany.

About 25 U.S. Army divisions landed at Vierville, which today has only 320 inhabitants. American troops advanced up the cliffs behind the Hardelays' house, where Germans were resisting the onslaught and where today French Gendarmes stood about every 15 feet as protection during Mrs. Reagan's visit.

Seated at a table looking out on Omaha Beach, Mrs. Reagan ate a lunch of lobster, sherbet in Calvados, turbots a la Normandy, Camembert and ice cream with strawberries and whipped cream. There were two wines, a 1978 Macon and 1976 Saint-Emillion.

Mme. Hardelay said later that the lunch was catered and that preparations for it were begun only 10 days ago. Describing Mrs. Reagan as "very charming," she said the first lady ate some of each course and "nearly all of her sorbet Calvados" (for "digestive purposes").

French Minister of Post, Telephone and Telegraphe Louis Mexandeau burst into song near the end of the meal in a rendition of an old Normand folk song that started, "I want to see again my Normandy."

At her table, de Beranger giggled and said: "Normand people have a reputation for singing out of tune."

Among the guests were Alex Gobin, the region's governor, Franc,ois d'Harcourt, a member of the French Chamber of Deputies, and U.S. Ambassador Evan Galbraith and his wife, Marie.

In a toast to Mrs. Reagan, d'Harcourt noted that it was the first time an American first lady had visited that part of France.

"It's an honor and pleasure to have you here representing the chief executive of the United States," he said. "We have great respect and admiration for your husband and what he stands for and is trying to do. He's the man the world needs today and is a great president."

After seeing photographs of Vierville taken during the D-day landing that show the Hardelay house in the distance, and before she went by helicopter to meet President Reagan in Versailles at the end of the economic summit, Mrs. Reagan received a small painting of the beach painted by the mayor's father in 1938.

Outside, when she met reporters, she took questions for the first time during her four-day stay in France and defended her practice of wearing American fashion designs rather than French originals during the visit.

"I have a great admiration for them French originals ," she said, "but I usually wear American designs. You have to buy to promote your own country."

Of her visit to the cemetery, she said, "I couldn't help being very moved and very touched. It was a very emotional experience." Asked if she had been close to tears when she was speaking there, she said, "I probably was."