Bash your enemy with a big stick or rock.
probably more like fling feces and run lol if you want to get real technical about it... but i would guess that the first art probably wasnt anything really systemized were it was a paticular style more like a mix of hand and grappling techniques... when they didnt have the big stick and rock thing going on... which later led to the big over sized sword and rock lol
What was the first martial art in Europe?

Define martial art, and what evidence you need to say a martial art existed.

For example, the oldest surviving documented training manual for use of sword and buckler comes from the mid 13th century. You could argue that is the earliest surviving example of evidence.

While direct evidence of how the Roman gladiator schools were run has not been found, I would certainly qualify a school that taught people how to survive in the arena to be a martial art.

The systematic teaching of combat tactics to the Roman legions should certainly qualify. Plutarch mentions having to emphasize the thrust over the cut in use of the gladius.

Before that the education of Greek Hoplites, and in particular the education of the male Spartan citizens should qualify as a martial arts. The Olympics were competitions of martial skills....

Some say that there are some surviving Egyptian heiroglyphics that show people training with weapons.

So how far do you want to go back, and what do you need to define something as a martial art?

Blindside said:
While direct evidence of how the Roman gladiator schools were run has not been found

But see the recent book "The Gladiators: History's Most Dangerous Sport" by Fik Meijer. Review here (may require registration).
Television Review
Sword-and-Sandals Men With Back Story Revealed

The program is the first installment of “Into the Unknown With Josh Bernstein,” a new series featuring the genial fellow who made archaeology entertaining as the original host of “Digging for the Truth” on History.

Mr. Bernstein promises a broader focus in his latest series, though that’s hardly necessary; ancient history has plenty of mysteries that could use his lively approach. In this episode, of course, his concern is the Roman Empire, and his premise is that those gladiators familiar from the movies are only part of the story, and what we know about them is not especially accurate.

That’s no surprise — when has Hollywood ever not distorted history? — but it’s a decent enough excuse to explore the far more interesting and more nuanced reality. Mr. Bernstein begins at a gladiator school in Rome, even doing a little gladiating himself. (Why is there a school to teach ancient gladiator skills? Who knows?) But he is smart enough not to let that silly bit go on too long, and soon we are hearing from well-chosen experts, including some who have found what they believe is a gladiator graveyard.
What was the first martial art in Europe?
Please be more difinitive in your question. It's too broad and, as currently stated, probably cannot be answered. Do you want to restrict to a time-frame or specific culture?

Peace favor your sword,
Some say that there are some surviving Egyptian heiroglyphics that show people training with weapons.
Well, it's not Europe, but close enough for such a vague question.

There are, indisputably, Egyptian artworks depicting weapon training. There's also the art depicting a wrestling match or wrestling Lexicon in the tomb of Beni Hassan (and variants of spelling). That is more controversial because some wrestling enthusiasts use it as a basis of a recontructed style of wrestling. Just under 100 or so different grappling techniques are illustrated, however, only about 2/3 to 3/4 of them are well enough preseved to figure out what they're doing.

There are also depictions of war and martial training in the remains of all of the Fertile Crescent civilizations as well.

Peace favor your sword,