I am not an expert by any means, but I have more than a passing interest about certain aspects of history, and seeing as it's been 9 hours and nobody has posted anything, I'll at least give it a shot and try to shed some basic light on the atmosphere and goings-on of the holiday through the occupation. Like I said, I'm not really a historian, I just like browsing this sub. If this post isn't acceptable because of this, I'll delete it by all means, but I figure an answer by me is more helpful for you than no answer at all.
It was dreary, gloomy, and depressing, but the people still had hope. The years during the occupation were the only ones in which a parade was not performed on Bastille Day in France (though there were parades in London, Algiers, etc), and any celebration seems to have been kept subdued by the occupation. The Nazis purposely beefed up their measures to quell any possible uprisings on a day with such significance in France.
However, like I said, the people still had hope. Allied bombers dropped millions of messages to the French promising freedom. In 1942, there was an attack coordinated by the French which killed 700+ Nazi forces, including many in command, in Yugoslavia. Meanwhile, in France itself, many more small instances of subversive attacks and sabotage...
Stricter restrictions were put in place in order to subdue any possible action by French resistance, and any male family of known French saboteurs or "anti-German assailants" would have to surrender or be shot on sight. Despite this, a steel mill was blown up, flax intended as rations for German soldiers was burned, many railroads were destroyed and sabotaged, thousands attempted to parade, leading to fights in the streets, and many other isolated incidents of unrest against the occupation were evident.
By 1944, the liberation of Paris was only weeks away and the people could feel it. Resistance was more overt than it had been, as war had come to France. Parisians started to very actively resist the occupation, and as the Allied armies advanced and soldiers were moved to the lines, the French resistance was finally able to more effectively combat their invaders. There was still no parades as Paris was becoming a warzone, but the atmosphere definitely changed from one of fear and uncertainty to real hope. Less than a month later, Paris was freed.