The moment came as the heads of state were talking to members of the crowd during an emotional ceremony on the anniversary of the end of World War One.
Merkel and Macron held hands as they shared a touching moment at the ceremony on Saturday near the town of Compiègne in northern France.
They had signed a book of remembrance in a railway carriage identical to the one in which the 1918 Armistice was sealed. Both leaders also unveiled a plaque to Franco-German reconciliation and laid a wreath during the visit.
After unveiling the plaque the two leaders began shaking hands and speaking with locals who had come to witness the event.
The 101-year-old woman, who had been watching the memorial, first enthusiastically grabbed Macron's hand. “Monsieur Macron! That is not possible! A little woman like me shaking hands with the President of the Republic. That's fantastic!” she said.
Then she greeted Chancellor Merkel by saying: “You are Madame Macron!”
Angela Merkel and Emmanuel Macron share a touching moment on Saturday. Photo: DPA
“No, I am the Chancellor of Germany,” Merkel, who was accompanied by an interpreter, explained to the senior citizen, initially in German.
But the woman still didn't seem to know who she was speaking to, so Merkel tried the same sentence again in French.
“Je suis la chancelière allemande,” she said.
At this point it was still not clear whether the woman understood who Merkel is.
Macron then asked the woman to look to the cameras for a photo.
The woman said “C'est fantastique!“, before Macron kissed her goodbye. She assured him that she would be at next year's commemoration.
The amusing and touching encounter, which was reported by German media on Monday, can be seen in full length in this video.
World leaders marked 100 years since the end of the Great War in a series of events over the weekend.
Around 70 leaders including US and Russian Presidents Donald Trump and Vladimir Putin attended centenary commemorations of the 1918 Armistice in Paris on Sunday.
“This day is not just about remembering, but should be about a call to action,” Merkel said Saturday after visiting the forest clearing in northern France where the Armistice was signed.