Trench warfare more or less ended with the First World War. Gas weapons were developed and deployed as a means of breaking the stalemate. To explain this, One must remember that WWI started almost at the turn of the century. Machinery and technology had made several breakthroughs. The implication of that tech though was made using 19th century tactic. Essentially, we found out how to kill faster but had not figured out how to move men faster. The armies of both sides could not take the losses of attacking each other openly and so more or less began to siege the other in the trenches. Gas was effective because there was a stationary target.
Such battles began with artillery barrages. Some of those shells would be gas. After that, stormtroopers would begin to clear out the enemies inside the trenches that survived. General infantry would follow with heavy weapons like machine guns and mortars and fortify captured positions.
The Second World War saw the birth of what we know as combined arms. The advent of the tank permanently changed war. With essentially a mobile pillbox that can go with the infantry, trench warfare was quickly found to be useless. Tanks were big enough and fast enough to roll over and past the trenches. Once past, they could then destroy headquarters, supply dumps and other essential structure. Combined with far better radio equipment, the Germans invented the Blitzkrieg or Lightning War. Now able to communicate with bombers and artillery directly, frontline commanders could order precise, powerful attacks.
No longer shackled to slogging through enemy lines on a broad scale, the Germans would target specific points and breakthrough. Once a hole was made, the enemies on both sides would be vulnerable to being outflank or entirely surrounded by a much faster army. The Blitzkrieg was quickly adopted by the Americans and other armies. With speed now the focus of armies, the time needed to create the trench systems of the First World War was no longer available. Trenches were replaced by the smaller and more easily made foxhole. With no targets held stationary by complex defenses, gas also left the battlefield as a viable weapon.
To answer your question, No gas was never used to my knowledge in any battle in the European Theater of Operations.
The Devil saw me with my head down and got excited. Then I said Amen