Wanting independence for Basque regions of France and Spain, and a "Basque country" means wanting to create a Basque nation. The people who demands such a thing usually do so because they identify themselves as Basque (or Breton or Catalan...) and not as French or Spanish. The same as most people in Europe identify themselves as French or German or Spanish and not Europeans. This is exactly what nationalism is. It serves to oppose people and has been the cause of wars, political rivalries and prejudices.
By the way, before you accuse me of not knowing what I'm saying, you should read what I write properly. I'm sorry I cannot write it in Spanish or Basque to make it clearer. I did not say Europe was unified, I said we should try to unify it. Of course, we cannot support the creation of new boundaries and the removal of existing ones at the same time...
You have been quite insulting in your comments: I'm not Spanish (therefore not brainwashed, lucky me) so in your opinion, I must be one of the "extreme right sympathetics". This is quite an insult for me (calling any one an extremist of whatever is insulting). Also, did you know that nationalists usually vote for extreme right political parties in Europe?
Basque citizens in France (and I believe in Spain too) have the same rights as every other citizen, including the right to demonstrate. I'm glad the Spanish Basque separatists moved toward peaceful actions in the last few years.
I'm sorry I do not support separatist actions as I do not believe the Basques are oppressed in France (nor in Spain, but I'm no expert). Maybe a better recognition of languages and particularities (administrative acts in two languages for example)...