Absolutely nothing you just said made any sense.
I never said anything about "Mongols staying in Europe". I was referring to all the hordes coming from the east, most of them actually Turk or other central Asian tribes and not mongols. Like the Huns, then the Avars, then the Magyars and their Turk tribe friends (Kabars and Onogurs), then the Pechenegs, then the Kipchak, then the Mongols, then the Tartars, then Ottomans,... we know how some of them completely crushed the Eastern-European "states" (Rus counries, Hungary,..) and Balkan "countries" and hindered progress in these regions, and if it wasn't for the HRE (and in some cases also Poland and Lithuania) all of Europe would have been at risk. In most cases it was the strength of the HRE that allowed none of these hordes to enter Western Europe (except for the Huns 300 AD but they were eventually crushed and driven off), just look what happened to Rus states during the 300 years of Mongol control...
People completely fail to understand how important the 1000 years of the HRE were for Europe, especially for Western Europe. It wasn't united? It was a federation, and that was for the good of Europe. So many things we think of today as "typical European" are the result of that system and the cultural influence the HRE had. It brought little culture? Yeah sure, except that pretty much all old European cities are from that time, that many of our traditions have their roots in that age, ... oh please, shut up.
"They also didn't win many wars since they lost to the Mongols in Hungary"
What the fuck are you even talking? "They" won countless wars, in fact they never lost to any invader or outer threat, the thing that brought the HRE to the brink of its existence were inner conflicts (especially the 30 years war), but it were these inner conflicts that shaped large part of Central and Western Europe to how we know it today and lead to important reforms that allowed Europe to progress.
Lost to Mongols in Hungary? The HRE never even fought a direct battle against the Mongols of the Golden Horde. Beside the many battles in Eastern Europe between the Mongols and the Rus states, Lithuania and the Kipchak, and the battles on the Balkan, it only came to two battles in "main Europe": In the first battle it was the Polish Kingdom (supported by Bohemia, Silesia and some crusaders from the Templar order, the Teutonic order and the Johanitian order) and in the second battle it was the Kingdom of Hungary (supported by some Bohemians (basically Czechs), Serbs, Vlachs (basically Romanians), Kipchaks (a Turk folk, previous invaders, had to flee from the Golden horde though many actually already joined the horde) and a few crusader knights from the Templar order and the Teutonic order) who fought and lost against the Mongols. The HRE actually prepared one of the largest army of that age to stop the Mongols but it never came to a battle as the Mongols already turned around and left Europe (except for the Rus states).
Both, the HRE and France played extremely important roles in the history of Europe and if it wasn't for the reforms, "stability" and political structure that came with these two Empires Europe wouldn't have been able develop the way it did and take that dominant role in the world. Many of the later "empires" people mention here would have never been possible, it was that time that gave Europe the important advantage over the rest of the world.