While I generally oppose Holocaust denial laws, I think this post misses out on some important context. There are active nationalist, white supremacist, and anti-Semitic political and parapolitical organizations active in Europe right now. A tremendous amount of anti-Semitic and anti-foreigner/anti-minority activity is intimately tied up with Holocaust denial. And by many accounts, anti-Jewish sentiment is increasing in Europe in recent years. The purpose of Holocaust denial laws isn't to stop academic discussion of the topic (although that's often a byproduct), but to stop actual Neo-Nazi and similar nationalist and white supremacist organizations. They don't exist in a vacuum.
We might compare it to the Lost Cause movement in the U.S. during the 1860s-1960s (well, really, to present). While it would have certainly been an unconstitutional act and I don't think the government should have actually done it, we'd have all been better off if there had been laws banning the Lost Cause revisionism that portrayed the antebellum South as a place of racial harmony and defending southern secession as a righteous defense of states' rights and individual liberties. These beliefs continue to distort American race relations, and many people continue as a result to have an incorrect and ahistorical view of the South, Reconstruction, and the Civil War (doubtlessly some readers are considering hopping in here and, wrongly, insisting that the Civil War was not actually about slavery, but hopefully this note will deter).
I think the motivation in European nations with Holocaust denial is aimed at heading off that kind of thing. There was a terrible event that was the culmination of decades of anti-Semitism in Europe. Many groups are, sometimes very explicitly, trying to revive that atmosphere, and part of the way they are doing it is by downplaying or erasing entirely the results of that kind of racist or nationalist ideology.