Not yet, the Euro has been a strong rival in recent years, and with good reason.
What is happening is that the dollar if falling relative to some other currencies. That is, if you exchange dollard for Euros, you get fewer Euros today, than you would have a few years ago.
What that means is that American exports are becoming more price-competative in those nations, and imports from those nations are becoming more expensive here. That's good for American producers in direct competition with European producers.
However, that positive effect is being undercut by other nations, like Japan, and to a much more significant degree, China, who are keeping thier currencies pegged to the dollar. The Japanese keep the Yen in rough parity with the dollar, while the Chinese keep the Yuan artificially depressed. The reason is that they are both major trading partners, and don't dare let the price of thier exports rise. China competes mostly for lower-value goods, so they must keep the yuan /very/ low to make up for the costs of shipping such goods across the Pacific. Japan produces higher margin exports, like cars and electronics, so is not obliged to savage thier own currency as severely.