Because the question was only asked in 2004, sample sizes are not as optimally large. The French figure should be seen as suggestive at best. Yet the results have face validity.
The Irish percentage is a little lower than expected. Those of Irish descent are unique among whites in that they have their own ethnic holiday (never mind that St. Patrick was actually British) and benefit from mild, if light-hearted, cultural encouragement in the celebration of that heritage (ie, "Kiss me, I'm Irish" or Riverdance). Like Italians, the disdain their Catholicism brought in the 19th and first half of the 20th Century doesn't hurt, either.
Germans, despite their ancestral homeland's oh-so-atrocious relatively recent history, were forced to suffer the humiliation of anglicizing their surnames during the Great Wars and dropping their purely Teutonic tongues to integrate with broader American society, so in the oppression pecking order, they're a notch above the English.
Those of British ancestry, without claim to historic oppression--Roman legions and the Danegeld are negated by the slave trade the Empire waited all the way until 1833 to thoroughly outlaw--are left to wallow in the crapulence of massive achievement, and are consequently the least likely to think of themselves in racial or ethnic terms. Americans of Scandanavian descent are not far behind.
Despite Sacha Baron Cohen's best efforts, Eastern Europeans in the US are not completely embarrassed by their heritage. Wait, come to think of it, the question was only asked in '04, before Borat or Bruno came into existence and Ali G was just beginning his ascent to household name recognition. Perhaps those anti-Semites have been brought to heel in the interim!
Unsurprisingly, Italians are the most cognizant of their ethnic heritage. Among the European waves, they were impoverished latecomers. Further, they tend to be more easily physically distinguishable from other whites than those of English, French, or German descent are. Still, even this most ethnically conscious European group is far less racialist than are blacks, Hispanics, or Asians in the US.
GSS variables used: SOCID1, SOCID2, SOCID3, ETHNIC
* Respondent sizes vary slightly in some cases for each degree inquired about (most important, second most important, third most important). Those listed in the table represent the smallest number of responses from the three parallel questions.
** British includes those of English, Scottish, and Welsh descent.
^ Scandanavian includes those of Danish, Swedish, Norwegian, and Finnish descent.
^^ Eastern European includes those of Czeckoslavakian, Hungarian, Polish, Romanian, and Russian descent.