I will admit that my familiarity with private law outside the USA is almost non-existent, except for what I skimmed from the Wikipedia article for the Inquisitorial system. So I had assumed that private law in European jurisdictions would follow the same judge-intensive approach. Rereading the article more closely, I do see that it really only talks about criminal proceedings.

But I did some more web searching, and found this -- honestly, extremely convenient -- article comparing civil litigation procedure in Germany and California (the jurisdiction I'm most familiar with; IANAL). The three most substantial differences I could identify were the judge's involvement in: serving papers, discovery, and depositions.

Serving legal notice is the least consequential difference between California and Germany, but it seems that the former allows any qualified adult to chase down the respondent (ie person being sued) and deliver the notice of a lawsuit -- hence the trope of yelling "you have been served" and then throwing a stack of papers at someone's porch -- on behalf of the complainant (person who filed the lawsuit). Whereas German courts take up the role themselves for notifying the complainant. Small difference, but notable.

In Germany, the court, and not the plaintiff, is required to serve the complaint on the defendant without undue delay, which is usually immediately after it has been filed with the court.

Next, discovery and pleadings in Germany appear to be different from the California custom. It seems that German courts require parties to thoroughly plead their positions first, and only afterwards will discovery begin, with the court deciding what topics can be investigated. Whereas California allows parties to make broad assertions that can later be proven or disproven during discovery. This is akin to throwing spaghetti at the wall and seeing what sticks, and a big reason this is done is because any argument that isn't raised during trial cannot be reargued during a later appeal.

I believe that discovery in California and other US States can get rather invasive, as each party's lawyers are on a fact-finding mission where the truth will out. The general limitation on the pleadings in California is that they still must be germane to the complaint and at least be colorable. This obviously leads to a lot of pre-trial motions, as the targeted party will naturally want to resist a fishing expedition during discovery.

Lastly, depositions in Germany involve the judge(s) a lot more than they would in California. Here, depositions are off-site from the court and conducted by the deposing party, usually video-taped and with all attorneys present, plus a privately hired stenographer, with the deposing attorney asking questions. Basically, after a deposition order is granted by the judge, the judge isn't involved unless during the deposition, the process is interrupted in a way that would violate the judge's order. But the solution to that is to simply phone the judge and ask for clarification or a new order to force the deposition to continue.

Whereas that article describes the German deposition process as always occuring in court, during trial, and with questions asked by the judge(s). The parties may suggest certain questions by way of constructing arguments which require the judge(s) to probe in a particular direction. But it's not clear that the lawyers get to dictate the exact questions asked.

In contrast, depositions in Germany are conducted by the judge or the panel of judges and only during trial.

I grant you that this is just an examination of the German court proceedings for private law. And perhaps Germany may be an outlier, with other European counterparts adopting civil law but with a more adversarial flavor for private law. But I would say that for Germany, these differences indicate that their private law is more inquisitorial overall, in stark contrast to the California or USA adversarial procedure for private litigation.