The French-American academic, 51, was in a hospital recovering from a gunshot wound. Before the other men got involved, Moogalian tried to take away the suspect's rifle but the man shot Moogalian in the neck with a Luger pistol, his wife, Isabelle Risacher, told France's Europe 1 radio.
He'll receive his own Legion of Honor when he gets better, the French government has said.
British passenger Chris Norman, who helped tackle the gunman, also received the award during a ceremony at the Élysée Palace.
"By their courage, they saved lives," President François Hollande said. "They gave us an example of what is possible to do in these kinds of situations."
Authorities have said a massacre might have occurred if not for the heroics of the men who attacked the suspect aboard the high-speed Thylas train traveling from Amsterdam to Paris last Friday.
The alleged gunman, identified as Moroccan national Ayoub El Khazzani, carried an AK-47 assault weapon with nine magazines of ammunition, a Luger pistol with extra ammo and a box cutter, French Interior Minister Bernard Cazeneuve said.
Four people were injured, with Moogalian being the last one still in the hospital, authorities said. His wife said he's in stable condition.
Risacher told France's Europe 1 radio her husband was quickly suspicious of the suspect because he entered the toilet with his suitcase and stayed inside a long time.
"Sometime later, the man came out and it is there (her husband) saw that he had a weapon," she said. "My husband ran to the man to remove his weapon."
'I'm hit, I'm hit'
During the struggle over the rifle, the suspect shot Moogalian in the neck with a Luger.
"I did not see the gunman because it happened too fast and I was hidden behind the seats," she said. "My husband collapsed, I saw him through the seats. My husband looked at me and he said, 'I'm hit, I'm hit.' He thought it was over and that he was dying. There was blood everywhere."
Stone was badly cut in the struggle but was still able to help Moogalian by putting pressure on his neck to stop the bleeding.
Moogalian's sister, Julia Moogalian, spoke to CNN on Monday and thanked Stone for saving her brother's life.
"My brother may not still be here if it weren't for him," she said. "He was selfless in staying there with my brother. Our family is very appreciative."
A biography on Moogalian's website
says he was born in Durham, North Carolina, and that his family later moved to Virginia.
As an adult he moved to France where he worked as a translator and English teacher for business professionals. His website says he's a artist, teacher and musician and recently published a novel.
Moogalian has dual citizenship and has been living in France for almost two decades, Julia Moogalian said. He traveling on the train with his wife and their dog, Benny.
Three buddies on vacation
Sadler, Stone and Skarlatos reportedly met in middle school in California and planned on spending the summer sightseeing together. It was Sadler's first trip to Europe, and National Guardsman Skarlatos was on a month-long break after serving in Afghanistan. Stone is an Air Force serviceman.
The three men, plus Norman, were in the same train car when gunfire erupted. Shortly afterward, a shirtless man appeared with a gun slung over his shoulder. He'd already struggled with Moogalian and another man who has not been publicly identified yet.
"He never said a word," said Sadler, a student at California State University in Sacramento. "At that time, it was either do something or die."
They charged at the gunman, and a fierce struggle ensued.
"He kept pulling more weapons left and right," said Stone, his arm in a sling from injuries suffered in the struggle. "He seemed like he was ready to fight to the end. So were we."
They punched the suspect, choked him and hit him with his own weapons. They finally restrained him before the train pulled up in Arras in northern France.
Stone tackled the attacker first. He was hospitalized and released.
"It is clear that their heroic actions may have prevented a far worse tragedy," said President Barack Obama, who phoned the three Americans.
Norman, the Briton
, said he was honored to receive the medal and ecstatic to be alive, along with all the passengers on the train.
"I am happy that no one got hurt," he said. "Spence and Alek are the two guys who we should really thank the most because they were the first ones who actually got up and did it."