Yes, Europeans definitely practiced martial arts.

The earliest European martial arts manual yet discovered is I.33, a German text which depicts fighting with arming sword (your basic cruciform one-handed European sword) and buckler (a small metal shield about the size of a dinner plate). This dates from the early 14th century.

It seems to have been intended for a general audience, as opposed to knights/nobles.

Next we have the work of Fiore De'i Liberi. He wrote around 1400, in Italy, and we have three copies of his manual in various states of repair. This may be more what you are looking for, as it also covers unarmed combat in addition to dagger, sword (in one hand and two), spear, poleaxe (a long-handled warhammer type weapon very popular in the 15th century), fighting in armour and out, and mounted combat.

The most complete version seems to be an attempt at a comprehensive martial art, applicable to duelling, self-defence, and war.

So yes - Europeans definitely had access to manuals and know-how covering martial arts. The examples we have from the (late) medieval period appear to be indigenous European arts. I don't believe there's any evidence of non-European martial arts being practiced or studied in medieval Europe. That obviously doesn't mean it didn't happen, there was trade with non-European peoples, so it was possible, we just don't have any direct evidence of it.