The double-axe carried a lot of symbolism in the bronze age, particularly in Greek and Minoan cultures. This symbolism was connected to its use a sacrificial instrument, so it's significance was likely more religious than military.

Northern Europeans made a lot of use of axes as weapons, but the classical double-axe, or bipennis, was not a big thing in those cultures. I can't find much in my more recent books, but John Hewitt (Ancient Armour & Weapons) says:

The double-axe is of still more rare occurrence in book-paintings... In the graves, the bipennis has never been found at all... Neither is it seen in the hands of the Anglo-Saxons in the Bayeux Tapestry.

He does follow with some comments on the very rare double axes that had been found, although even they did not follow the symmetrical plan of the labrys. He describes one in which the two axe blades are set perpendicular to each other (so more of an adze-axe than a double-axe), and concludes that it was more likely a workman's tool than a weapon.

However, if you're willing to stretch your definition of the double-axe a bit, dual-headed (or even triple-headed) weapons with axe blades were actually very common in medieval european armouries. It's just that the 2nd head was generally not another axe, but a hammer or spike or somesuch. Battleaxes, poleaxes, halberds, and various related weapons followed this plan: broad chopping blade, backed by an armour-piercing hammer spike, sometimes with a spear-like thrusting point set between them.