In Spain, the renewed vigor of the Catalan secessionists movement is gaining a lot of international attention. The Basque independence movement also appears to be gaining political traction in Spain.
In Belgium, there seems to be little but spit, bubble gum, and a common monarch holding the linguistically divided country's two regions and its mixed leading city together.
Scotland has been making noises of late about gaining greater autonomy, and already has considerable independence in practice from England, with its own legislature, its own judicial system, and a variety of very different laws and governmental institutions than its southern neighbor within the United Kingdom.
While I haven't heard any recent news from Italy, at time, its Northern regions (roughly corresponding to the parts of Italy that were never part of the Kingdom of Sicily), have actively campaigned for independence in the post-World War II era.
There may be other active and viable secessionist movements among E.U. member nations, but I'm not aware of them.
While obviously not European, Quebec for a long time was very keen to secede from Canada, although this impulse seems to have been quite muted in the last few years, and Quebec's French nationalist party took an immense blow at the polls in the most recent Canadian parliamentary election, if I recall correctly.
One theory that has been advanced to explain the rise in regionalism in Europe is that the possibility that the multiple countries arising from a divided country that is an E.U. member might all become members of the E.U. and thus not face all of the economic isolation and reduction in capacity to act collectively in the face of a crisis that a small sovereign state outside of a larger federation would have to deal with has made secession a more attractive option for E.U. member countries facing deep internal cultural divisions.
Another theory is that the break up of Czechoslovakia, the Soviet Union, Yugoslavia (and further Kosovo from Serbia), Ethiopia and Sudan in recent memory, have provided evidence that while splitting up a single nation-state into component parts may be painful, that it is not necessarily an intolerable price to pay for autonomy or impossible to achieve, particularly if it can be brought about by political means rather than an insurgency or military intervention.
While some of the divisions involve a deep linguistic divide, in other cases, the divide linguistically does not seem all that deep - just a difference in mutually intelligible dialects within a single language.