Not exactly. For starters, the French people at Versailles were mainly dealing with the German Empire rather than the Austro-Hungarians. Granted, the Treaty of Trianon and the Treaty of Saint-Germain would come deal with both halves of the Dual Monarchy (Hungary and Austria respectively) that same year, but for the French people their main enemy had been the German Empire on the Western Front. As a result, although there may certainly have been remarks about the Paris Peace Conference being compared to the Congress of Vienna (which, to be pedantic, was concluded 104 years earlier than the Treaty of Versailles), as far as my research on the matter has been able to yield, the mood of the French public at the time was one of uncertainty for the future and bitterness at the German Empire.

The national identity at the time of Versailles had shifted to be one of united struggle against the German invaders who had started the war (at least in the view of the French government) back in 1914. The populace had been mobilised, old religious and social divisions had been put aside, and previously neglected economic sectors were galvanised for the war effort. The French nation had endured four years of conflict that had ravaged entire provinces, razed settlements, and displaced millions of civilians. Ignoring for even a brief moment the amount of French casualties sustained in the First World War (estimated, for combatant soldiers, to be between 1.3 - 2 million), there was no outpouring of pride that the Austro-Hungarians, or even the Germans, had been brought to negotiate at the mercy of the French as the Bonapartist regime had to in Vienna.

Sedley Lynch Wane, writing on the effect of the First World War on France as a nation, notes the following during the Paris Peace Conference:

"One of the worst evils resulting from the war is that German militarism and its methods have stamped on French souls bitterness, fear, and ineradicable distrust."

The French were also divided over the Treaty of Versailles. Whilst many expressed joy at the "rightful transfer" of Alsace-Lorraine back to France, as well as the demilitarization of the Rhineland, several radical politicians and groups expressed concern that Germany would never abide by the reparation terms or even the military restrictions. To them, the only way the Germans could be held responsible to the terms was by the "use of force" as British Prime Minister David Llyod George put it. What did resonate with the French however, was the bitter memory of a peace settlement which, and not by coincidence, shared the same name as the one which they presented to the Germans in 1919: The 1871 Treaty of Versailles. This peace settlement had ended the Franco-Prussian War, and it is a curious parallel that the German Empire which had been proclaimed in the Hall of Mirrors at Versailles was, in 1919, no longer a polity in the Hall of Mirrors (replaced by the Weimar Republic).

Hope this brief response helps with the question, and apologies for the lack of primary sources (somewhat harder as they may be to come across) on the matter. The secondary ones below should go some way further to "painting a picture" of the French mood in 1919 however, and why the Congress of Vienna seemed like a settlement from a bygone era to the Third French Republic at Versailles.

Sources

Barnes, Harry Elmer. "The Public Significance of the War-Guilt Question." The Annals of the American Academy of Political and Social Science 175 (1934): 11-18. Accessed March 6, 2021. http://www.jstor.org/stable/1020691.

Geo A. Finch. "The Peace Conference of Paris, 1919." The American Journal of International Law 13, no. 2 (1919): 159-86. Accessed March 6, 2021. https://www.jstor.org/stable/2188076.

Seymour, Charles. "Policy and Personality at the Paris Peace Conference." The Virginia Quarterly Review 21, no. 4 (1945): 517-34. Accessed March 6, 2021. http://www.jstor.org/stable/26441987.

Ware, Sedley Lynch. "Some Effects of the Great War upon France." The Sewanee Review 30, no. 2 (1922): 179-91. Accessed March 6, 2021. http://www.jstor.org/stable/27533535.