Many Canadians perished in the Battle of Vimy Ridge, in April 1917, when four members of the Canadian Corps received Victoria Crosses.
Despite the courageous deeds and sacrifice honoured by the Vimy Memorial, the couple are believed to have stripped naked and performed sex acts beside the soaring stone structure.
They then posted the video on a website, invited people to pay to watch it.
Their punishment came just six months after another couple were fined for taking nude photographs of themselves in the same place.
In the latest case, heard at Arras criminal court, involving the married couple, who are in their 30s, lawyers expressed concern at the gradual increase in such incidents at the memorial.
The prosecutor, Elise Bozzolo, said: “The memorial has been known for a long time as a place where exhibitionism and voyeurism is common.”