One of the French fencers in the 1896 Olympic Games was named Henri de Laborde. No other facts are known about this fencer. But it is very interesting that he has the same, somewhat rare name as Prince Henrik's grandfather and since the grandfather was born in 1868, he would have been at a reasonable age to have competed in 1896.
Since the 1896 Olympics were the first modern Olympics, they were not as famous as they are today. It wasn't until the 1936 Olympics that they became a major media event. As a result, many of the athletes who competed in the earlier Olympics considered them just another tournament and did not make a big deal about competing in them. Since the grandfather died in 1929, he could have competed but never mentioned it.
Is it known whether Prince Henrik's grandfather fenced? Any record of his traveling to Athens in 1896? There exists a picture that was taken of the French fencers at the 1896 Olympics but it is a group picture and they are not identified by name. Is there a picture of Henrik's grandfather, especially when he was in his 20s or 30s, that can be used to see if his face matches any faces in the picture of the French Olympic fencers?