Has an Euros game ever ended 4-4?
It has. 4-4 has been a Euros final 3 times in 3,212 games. The first was Yugoslavia and Wales drew on December 15, 1982; the latest was Belgium and Austria drew on October 12, 2010.
That makes 4-4 the 26th most common final score out of 34 that have ever occurred in Euros. One point away, 5-4 has happened 1 times and 4-5 has happened never. At one point the score disappeared for 28 years, between 1982 and 2010.