There are multiple EEPs which have a clear re-introduction/in situ component for European fauna. I would assume they would adhere to your standards of a legitimate breeding program. These are:
Montseny brook newt
European pond turtle (dedicated breeding centres in multiple zoos)
Waldrapp ibis
Bearded vulture
Cinereous vulture
European griffon vulture
European mink (dedicated breeding centres in Tallinn and Zoodyssee)
Eurasian lynx
Przewalski horse
Wisent
European forest reindeer
Alpine ibex
Not in an EEP framework, but still used for re-introductions is the marbled teal.
There is a whole range of species for which one or a few zoos are working for re-introductions locally. This is often in collaboration with local nature conservation organisations and local governments. This includes, but certainly not limited to:
European (white) crayfish
Stone crayfish (Besancon and others)
Pond mudsnail (Edinburgh Zoo)
Crau plain cricket (Besancon & la Barben)
Longhorn beetle (Nordens Ark)
Alpine longhorn beetle (Alpenzoo)
Great capricorn beetle (Nordens Ark)
Rattle grashopper (Nordens Ark)
Clouded apollo (Nordens Ark)
Chequered blue (Nordens Ark)
Pine hoverfly (Highland Wildlife Park)
Rhone streber (Besancon)
European mudminnow (Tiergarten Schoenbrunn)
Fire salamander (Besancon, Gaiazoo and others)
European spadefoot toad (Artis)
European green toad (Cologne, Nordens Ark)
Pool frog (Kristiansand Zoo)
European tree frog (Riga Zoo)
Mallorcan midwife toad (Zoo Barcelona, ZSL)
Meadow viper (Budapest Zoo)
Sand lizard (Marwell and other British zoos)
White stork (Nordens Ark, Cotswold)
Lesser white-fronted goose (Nordens Ark)
Little bustard (Zoodyssee, Obterre, Villars les Dombes)
Eurasian eagle owl (Nordens Ark and others)
Ural owl (Tiergarten Schoenbrunn, Tierfreigelaende Bayerischer Wald and many other Central European zoos)
White-backed woodpecker (Nordens Ark, Jarvzoo, Skansen)
Harvest mouse (Besancon)
European hamster (Gaiazoo, Diergaarde Blijdorp, Heidelberg and many others)
European garden dormouse (Gaiazoo and others)
Hazel dormouse (Wildwood Kent)
European souslik (Tiergarten Nurnberg and others)
European red squirrel (Loads of British zoos)
Scottish & European wildcat (RZSS and others)
As
@Therabu mentioned, many of these species are common throughout most of their range, but have gone extinct/are very rare at the edge of their natural range. There are of-course exceptions such as the Rhone streber which is a critically endangered fish known only from a tiny area in France and adjacent Switzerland.
As always there are a few zoos taking the lead with a larger number of species. Then there are species kept by quite a number of zoos, but again most zoos contribute little except from a few vultures.
There really is scope to do a lot more in terms of captive breeding of rare European species. Nordens Ark shows how much success is possible with invertebrates. Additionally there are plenty of freshwater fish in need of captive breeding. And with small mammals there is plenty of potential too. The starting of a breeding program for Bavarian pine vole is a start, but that a species like Pyrenean desman isn't kept in captivity is somewhat surprising to me....