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A sign in East Village Wines informs customers that the wine and liquor store accepts payment in euros.

I am not worried about rich Arabs; it’s the French who worry me.” This was the response from a businessman in Clovis, California, reacting to my comment that the U.S. government was concerned about the influence of foreign-owned sovereign wealth funds.

“Why are you worried about the French?” I asked.

“They just bought the largest company here,” he replied. “Life will now change for all of us—that company has been an important part of this community for years.” He was referring to Pelco, a Clovis-based manufacturer of video security systems that was recently acquired by Schneider Electric, a French company.

There is nothing special about Pelco’s sale; foreign companies buy American ones all the time and vice versa. This transaction was far smaller than the United Arab Emirates’ $7.5 billion investment in Citigroup or China’s $3 billion investment in the Blackstone Group, a major financial company. Except that this transaction is part of a trend that, though still largely unnoticed, will soon rear its head: The United States is poised to receive a massive—perhaps unprecedented—inflow of large- and medium-size European investors. Everything from corporate behemoths to family-owned companies are about to come to America on a corporate buying spree. Call it the Euroinvasion. Not only will many U.S....