Is Holocaust denial just a modern issue, or were there Holocaust deniers directly after WWII as well?

I can speak specifically to French revisionism in the immediate post-war era (so 1945-1970s).

The short answer is yes, kind of: there was Holocaust denial among a significant number of French people in the sense that there was a concerted effort, primarily among Pétainistes (those who aligned themselves with General Pétain, the WWI hero who was the head of the French puppet government during occupation), and later Gaullistes seeking to repair France's image in the post war era, to minimize the extent to which French collaborateurs aided the Nazis in identifying, rounding up and deporting French Jews.

They didn't outright deny that La Shoah happened. Some justified their involvement in the Holocaust because in their view without cooperation the Nazis would have gone "total war" against France during occupation, similar to what happened with Poland. But the truth is that at the time France was quite anti-Semitic, perhaps just as anti-Semitic as Germany, and many French people had little issue ridding their country of their Jewish neighbors. So in the decades after WWII in France, there was much debate over whether collaboration with regard to the deportation of Jews was done out of necessity or eager willfulness. In short - little bit of column A, little bit of column B.

Of course this pervasive European anti-semitism fell more out of fashion as the 20th century progressed. Which brings us to the idea of Résistancialisme: the inflated national myth of the role that the French resistance played in aiding the allies in toppling the Nazis. There was indeed a French resistance, primarily comprised of elements of French society that tended to be more on the fringes: students, communists, anarchists, liberal Catholics, but it was by no means something that every French citizen subscribed to or believed in during occupation. Charles De Gaulle and his Gaulliste successors attempted to bolster this idea of a unified national French resistance that worked to prevent the deportation of Jews and aid the allies. If you're American it's sort of similar to how some in the US might say that the citizens of the Northern states during the Civil War were all ardent, morally-driven abolitionists, which isn't quite true.

In the context of the French, the outright denialism that you are thinking of - that the death toll of the Holocaust is either exaggerated or that the Holocaust outright didn't happen - didn't manifest itself in the realm of public debate until the early 1980s with what is now known as the Faurisson Affair. Robert Faurisson, a professor, wrote an article for Le Monde entitled "The Problem of the Gas Chambers, or The Rumor of Auschwitz." He argued that the gas chambers did not exist, and that the death toll from the Holocaust was exaggerated. Faurisson was convicted of breaking laws against Holocaust denial. Noam Chomsky, who is Jewish, famously and controversially defended Faurisson on the grounds of free speech.

sources:

Wolf, Joan B. Harnessing the Holocaust. (Stanford : Stanford University Press, 2004)

Berger, François. « L’Exploitation de la main d’œuvre française dans l’industrie sidérurgique allemande pendant la Seconde Guerre mondiale. Revue d’histoire moderne et contemporaine. Vol. 50, No. 3. (July-September, 2003)

Burrin, Philippe. La France à l’heure allemande. (New York: The New Press,1996)

Gordon, Bertram M. Collaborationism in France during the Second World War. (Ithica : Cornell University Press, 1980)

Dank, Milton. The French against the French. (Philadelphia : J.B. Lippincott Company, 1974)

Rousso, Henry. La hantise du passé. (Paris : Les éditions textuelles, 1998)