I'm assuming by "European Jews" you're referring to Ashkenazim, despite the fact that Sephardim, Italkim, etc. are "European Jews" as well (though are not "Ashkenazi"), so I'm going to answer this question regarding Ashkenazi Jews.
Ashkenazi Jews are descended from an elite group of Rabbinic scholars/merchants invited into the Carolingian domains by way of charters beginning in the Ninth Century CE in order to help the expanding Holy Roman Empire administer its newly established urban centers along the Rhine (namely the towns of Mainz, Worms, and Speyer). These select scholars/merchants were the heirs of the surviving network of schools originally founded by Rabbi Yochanan ben Zakkai in the aftermath of the fall of Jerusalem in 70 CE. Yochanan ben Zakkai, a colleague of Shimon ben Gamliel, was a student of Shimon's great-grandfather Hillel the Elder, a direct-line recipient of the Laws received by Moses at Har Sinai.
Today there are three major minhagim among the Jews; Ashkenazi, Sephardi, Teimani. When the redemption began in 1948, and Jews from all four corners of the earth were brought back to Israel, they all had the mezuzos in the same right side, the same Shema Yisrael inside, same tefillin, same tzitzis, same Seifer Torah; 99% of the customs the same. The migrations, persecutions, expulsions, pogroms; scattered few in number, every which way, and without any semblance of modern technology; still, Jews, defying the laws of history, kept one Torah, one mezuzah, one tefillin, one Shabbos, one circumcision. Even the tefillin that were found in the aftermath of the Bar Kokhba revolt (132-135 CE) have the same parchment that we use in tefillin to this day. It matters not whether one is Ashkenazi, Kavkazi, Bukhari, Teimani, Sephardi, Italki, Gruzini, Mizrachi, etc. A Jew is a Jew is a Jew. We are all brothers and sisters. G-d intended, earmarked the Land of Israel for us in our Torah. And when we have it, we are not allowed to give it away. The only One that can take the Jewish People off the land, is G-d Himself.