They tried, but like every participant in WW2 other than the US, the semiautomatic rifle developments came too late to have a realistic shot of replacing existing inventories. The German war machine during WW2 pretty consistently suffered from production shortages, and they were heavily dependent on captured equipment and factories to keep occupying forces equipped. The bolt-action Kar 98 benefited from the fact that it had established production lines already working at capacity and factories had been captured all over Europe - the FN factory in Liege, the Skoda works in Brno, and the Zastava factory at Kragujevic - that were producing variants of the Mauser 98 pattern. Even with the capture and eventual conversion of these factories to the K98 pattern, the Germans would gradually cut corners as the war went on to keep up with demand for rifles.

More importantly, the German semiautomatic infantry rifle program started too late and didn't produce something resembling a truly practical infantry rifle until 1943. The Gewehr 41 program was beset by a myriad of poorly thought out requirements and ultimately resulted in a very complicated rifle that was expensive and underwhelming. Mauser's design attempted to stick to all requirements and ended up a dismal failure with only a few thousand produced, and Walther's G41 ignored some of the stranger requirements (no visible moving parts, backup bolt action) but still suffered from reliability issues due to the decision to use a gas trap system in place of a more traditional gas piston. It did enter mass production, but at most fewer than 150,000 were produced - hardly enough to replace the K98.

The G43 that followed was a more sane development making use of a similar gas piston system to the one seen on captured Soviet SVT-40s. Along with a number of other improvements to the gun, the G43 was a substantially more practical infantry rifle. But by the time it was developed and ready for production, the war situation was already dire and transitioning to the new rifle wasn't feasible. Even with significant effort put into ramping up production, only about 400,000 would be produced by the end of the war.

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Really, the US was uniquely situated to adopt a semiautomatic service rifle before the war and was the only one with a realistic chance to do so. The French effort, like the Germans' started too late - their MAS-40 prototype had only a handful of examples produced for trials when France capitulated. The Soviets had their semiautomatic rifle program as well, and had every intention of replacing the Mosin Nagant with the SVT-40. But when the massive losses of men in 1941 led to a massive demand for rifles that SVT-40 production could not keep up with, the decision was made to swap production back to the Mosin. The US was in a unique position where production had become early enough and the industrial potential was both great enough and insulated from enemy forces, meaning factories could easily be tooled up to meet demand long before attrition on the front became an issue.