As already noted by the OP, many rare earths fluoresce under ultraviolet light
and there seems to be no particular reason why Europium is a better choice than any other element, purely based on its fluorescent properties. (See update at bottom)
The European Central Bank keeps the exact nature of the compounds used a secret. However, it was discovered in 2002 by Frank Suijver and Andries Meijerink  that europium, complexed with two $\beta$ diketone molecules provides the red light but the other colours were more difficult to identify.
However, the reason for the choice of Europium is unclear. According to Hugh Aldersey-Williams:
It [the European Central Bank] wilfully misunderstands my request to know who fought for Europium and drearily asks for my 'understanding that, for security reasons, we cannot comment on the chemical components of the euro banknote security features.'
Apparently, in the original paper by Suijver and Meijerink they say that they were visited several years beforehand by European Bank officials who were investigating potential luminescent materials so it may be that they inadvertently gave the bank the idea for using Europium in its banknotes.
Europium is one of the more expensive lanthanides and so this is probably a factor in its usage to prevent against forgeries, as the OP suggests.
I suspect there is also simply an element of irony in the fact that Europium is used in Euro bank notes and it may be that it was just some bank official tasked with finding a suitable compound to use who thought that it would be funny to use Europium.
Anyway, the bottom line appears to be that nobody knows the reason because the European Central Bank refuses to tell anyone anything about the compounds they use.
UPDATE: In response to @Nicolau Saker Neto's comment I did some more research into the fluorescence of Europium. Europium(III) (red) is regularly used alongside Europium(II) (blue) and Terbium(III) (green) in trichromatic lighting systems. It may therefore be the case that Europium was chosen because it is already well studied and in common use and that they created a $\beta$ diketone complex in order to fine tune the exact wavelength of the emissions and make it unique to their banknotes.
 http://dspace.library.uu.nl/handle/1874/25831 (Paper in Dutch which I can't read. However, Williams refers to some of the content in his book and I have alluded to this above. If anyone can translate the original paper and add anything to the answer that would be very helpful.)
Hugh Aldersey-Williams; 'Periodic Tales: The Curious Lives of the Elements'; ISBN 978-0-141-04145-2 http://www.amazon.co.uk/Periodic-Tales-Curious-Lives-Elements/dp/0141041455