The Knights Templar only really existed for around 200 years - and were originally set up, with a Papal blessing to protect Pilgrims to the Holy Lands. - However they became so rich and powerful - they were then disbanded.
Now, it all depends what you describe as "Europe" - and what's described as "The Holy Lands". The boundaries and countries of today, are not necessarily the same as they were then - and names have changed.
The Knights Templar were originally based in Portugal ( and so Europe), and were originally mainly French - but moved their headquarters to Jerusalem - then to Cyprus (which Island they briefly owned) - and ended up in France (Europe again) - when they became the target of King Phillip - who was heavily indebted to them - and was one of the principal instigators of their disbandment - for avaricious financial reasons.
Whilst the original intention was for the Templars (named after the Temple of Solomon in Jerusalem), to protect Pilgrims to the Holy Lands - such as Palestine - Squadrons of them did fight in battles on the Iberian peninsula (today's Portugal and Spain) - in battles known as the Reconquista. This means re-conquest - as much of those lands had been conquered by Islamists from around 770AD. This conquest ended by 1492 - with the Battle of Granada - which Templars also took part in.
It's all in that article - but I agree, it isn't easy to dig out the answer to your question - as many of the names of countries and borders have changed in the intervening thousand years or so. But the short answer - if you agree that Iberia is now in Europe - is ...................yes they did.
Hope that helps - jb