How does a US attorney, who has practiced law for 8 years, go about getting a European law degree with the objective of practicing law in France or another European country?

It will depend on the bar requirements in each country. For instance, in France a prospective 'avocat' needs to study for an undergraduate law degree (3 years) and then complete a diplôme de maîtrise en droit (that's a one-year program).

Then you'd take their bar exam; after that you'd pursue the 18-month long Certificat d'aptitude à la profession d'avocat (CAPA).

As far as I know, if you've passed a bar exam as a foreign lawyer, you may be able to shortcut through some of the educational requirements (going straight to the bar exam, then the 18-month long CAPA). However, there may be an additional educational requirement based on the fact France's legal tradition is different from that practiced in the US (Civil vs. Common Law...) You'll have to do some research on all of that, assuming you speak French...

Other European countries probably have similar requirements, but that's something you could look into based on the countries you're interested in (and the languages you speak.)