The FP7 projects PIONEURS (2003-2006) and EUCROSS (2011-2014) focused specifically on this question of European integration "from below". See the book "Pioneers of European Integration" (2009) by Ettore Recchi and Adrian Favell...
I don't think, a trans-european identity is new at all. I would go for an understanding of different types of european identities that developed -above all- since the early 20th century. In this reading, we would face nowadays a stronger than never trans-european identity - but not at all a loss of national or regional identities.
I guess it also depends on what we mean by “European identity”, which is certainly a contested idea (Does the meaning of Europe differ according to different people/regions within Europe?), and on which dimensions of identity (membership in a category/group or the attributes attached to that category, etc.) we consider.
In my view, this notion is relevant also because it has an impact on immigrants’ integration.
I just came across this interesting paper on measuring Europeanization: http://www.tandfonline.com/doi/abs/10.1080/.VBWajEvv-b8