The European monetary system was in place between 79 and the late 90s. It was a system, where each currency could be revaluated by +-2,25% each year. Soon the DM established itself as strongest currency and was raised in value almost every year, while currencies like the Lira (italy) were devaluated each year. It was flawed, because 2,25% of adjustment just werent enough, so after a short period of time, the DM was undervalued, while other currencies were rather overvalued. The national federal banks had to make sure, that their own currency isnt falling out of this corridor. In this context the german federal reserve did a lot of "sterilization" (e.g. buying foreign bonds while selling domestic ones)
In the 90s the system was so broken, that the rules were changed (+-15% were allowed each year). The UK joined for two years, but left soon after, because the system was clearly not working. Italy also left as well in 92.
A system, where the market could have set the exchange rates, would have been much better, but politicians always have to tinker with stuff.
When the EURO was introduced this very obvious problem was just ignored. Instead of a major adjustment (2,25%/15% each year) no adjustment was possible anymore. I have absolutely no idea why anyone thought, that this was a good idea. Its really mind-boggling.
here a DM/Lira chart for the time:
In the end its hard to answer the question of "where would the deutsche Mark" be today. Eventually somewhere around the value of the CHF, while the Euro would be worth a lot less. Germany would export less, while everybody else in germany would benefit from a strong currency. Its a myth, that a strong currency is a bad thing. Its spread by short-sighted politicians who dont understand the bigger picture. Undervaluing the currency is fairly popular, because it leads to visible short term gains, while the costs are hidden and diffuse.