Mountain weather is even more changeable than in other places.
Plan for everything.
+1 Plan for the worst and hope for the best
I have been to Europe every year since 2008, sometimes more than one trip, mainly the Alps (6 visits) but also to Black Forest and Pyrenees, only the trip to the Pyrenees was a bit of a washout, but I do not think any trip of more than about 4 days was entirely dry and most trips would involve at least one miserable slog through several hours of rain.
Overall I would say most of my trips have been 70%-90% dry, the statistics for most places will be along the lines of 1 day in 3 having rain, although this could be a 5 minute shower or an 8 hour deluge so the Stats are nothing more than a guide as to which months are historically better than others....
...also that 1:3 average does not mean you won't have 10 days of solid rain, but in reality 10 days of solid Sunshine are statistically more likely, basically it is a lottery - but one where the odds are stacked in your favour.
Mid June - Mid July or early September would be my advice for the Alps, it can be very hot in July and August, plus traffic will be heavier during School Holidays - but still much lighter than UK traffic so don't worry if you do have to go in August, I have done so a few times and still had a great time.