"In Europe the treaty is seen as a right wing document. "
That is media misinformation...
It would have codified an un-democratical, elitist, socialist welfare statist EU on all of Europe. An unelected Court would have had most of the power (sound familiar), and the document was so poorly written it was unclear who had what powers. Socialism was embedded in it: It had in its constitution a 'right' to employment outplacement services, 'rights' to health care, etc., for example. France's media whining about 'economic liberalism' is sleight-of-hand, the French didnt want to compete with low wage eastern europeans or see unlimited immigration ... same fears some have in the US, but that doesnt make the anti-immigration folks 'socialist'.
any connection between that EU Constitution monstrocity and concepts like democracy and freedom were purely incidental. It is a very good thing for freedom and for conservatives that this was rejected.