As far as I can tell there is no one single commonly accepted application process in Europe, despite what you might have read/heard/interpreted.
In my experience there are 3 ways to get enrolled in a PhD program in continental Europe:
You find a job advert at a uni where they are looking for a candidate to carry out (parts of) a project. In this case you are practically applying for a pre-determined job, and they assess you based on your skills, education and personality (for group chemistry)
You find a group you want to work for, based on your interests. You get in touch with a group leader/PI regarding your interest in doing graduate studies in that group/lab. If they have the money to recruit you and a project of common interest (a project that appeals to you and the direction that particular group is going with their research) you start there, often on a short term "trial period" initially (the actual/formal name of this period varies widely across the universities and countries)
You get invited to do a project at a group, with people you know previously. This occurs often if you do your master thesis/diploma work at that group, or if you know one of the prof.s at the department.
Beyond that, the formalities of what you need to write/submit in your official application would be specific to each uni I would guess.
EDIT: I have to actually correct myself, I do know people that had to pitch project proposals for graduate studies, however it still fits more into Option #2 above, where they got in contact with a group that worked on the field of interest and given that there's money for recruitment they were asked to formulate a short project proposal.
These people were applying for PhD positions in more humanitarian sciences however, one was going for behavioural/organizational economics and the other was more towards sociology I think.