No, this isn't some weird idea that he had kids with Eva Braun (or even one of the Moseley sisters) it's much more prosaic than that. It's that while he was a soldier in World War One he had an affair with one of the local farm girls while on leave. That led to a child and that child has gone on to marry and have children himself. The thing is though, that farm girl was French, so was the son and thus so are the grandchildren.
There are a number of amusements about the story, not least that Hitler's son actually fought against the Nazis and even joined the French Resistance:
"Incredibly, Mr Loret went on to fight the Germans in 1939, defending the Maginot Line before it was bypassed during the Nazi invasion which resulted in France being occupied from 1940 until 1944.
Mr Loret even joined the French Resistance, and was given the codename 'Clement'.
Just before her death in the early 1950s, Miss Lobjoie finally told Jean-Marie that his father was arguably the most infamous dictator in human history. "
Hitler never actually recognised the boy, now dead, as his son but did send money to the mother. And there are reports of German officers giving her money after the invasion of France.
"The new evidence which has surfaced after his death includes official army documents which show officers delivered envelopes of cash to Charlotte during the German occupation of France. There were also paintings signed "Adolf Hitler" found in her attic."
You can look at the photographs of Hitler and his claimed son here. I do think the moustache was probably a mistake if he didn't want to be recognised as the son though.
The family lawyer has pointed out that the grandchildren might be able to claim royalties on Mein Kampf. Which, under European law they could in fact: royalties last for 70 years after the death of the author over here and as Hitler died in 1945 the "work" does not become public domain until Jan 1 2016. There would be a bit of a fight about this as copyright currently belongs to the State of Bavaria and they won't allow it to be published in German or Germany (for obvious reasons) and while it is published in other countries they're not paying royalties on it as the Bavarians refuse permission for publication. Hitler's great nephew is said to have a good claim to whatever royalties there are but he refuses to pursue any such claim.
What does amuse is that a piece of British propaganda was that Hitler was monotesticular: a song to the tune of Colonel Bogey starting "Hitler, has only got one ball" being very popular during the war years. It wasn't true, at least no one knew that it was, Goering was the one who was as a result of an injury in the street fighting years. But if it was and if this story is true then we do know that even only that one was functional.
But think about it: would you really want to come out as being one of Hitler's grandchildren?