Contrary to popular belief, martial arts did not originate entirely from Asia and below is a list of European martial arts:

European (Uncategorized):

Shield Fighting
Jousting
Fencing

England:

Boxing
Quarterstaff
Singlestick
Catch Wrestling
Cumberland and Westmorland Wrestling
Devon Wrestling
Lancashire Wrestling

France:

Canne De Combat
Savate
Gouren
Bâton français

Germany:

Ringen
Unifight

Greece:

Pankration

Iceland:

Glima

Ireland:

Bataireacht
Dornálíocht
Coraíocht
Speachóireacht

Norway:

Stav

Portugal:

Jogo do Pau

Russia:

Sambo
Systema
Kulachniy boy
Retuinskih's System ROSS
Spetsnaz GRU Hand-to-Hand Combat Style
Spiridinovia
Ryabko's Systema

Scotland:

Scottish Backhold

Serbia:

Narodno Rvanje

Spain:

Juego del Palo
Keysi Fighting Method

Switzerland:

Schwingen

Ukraine:

Combat Hopak