Remember how we supposedly had that little sovereign-debt problem solved in Europe thanks to the hard work of Germany's Angela Merkel and France's Nicolas Sarkozy? Well, we may want to cancel the celebration dinner.

Pivotal elections in France and Greece over the weekend have the eurozone once again moving toward total failure.

In France, incumbent Nicolas Sarkozy was voted out of office in favor of Socialist Party nominee Francois Hollande, whose agenda involves reworking the region's debt-bailout package. Hollande favors considerably more government spending as opposed to many pundits who think France needs to considerably cut spending in light of its rapidly rising debt levels to GDP. If Hollande gets his way, France could also become the least wealthy-friendly country in the world, with a nominal tax rate of up to 75% on top earners.

Greece, a country that has already effectively defaulted on its debt obligations and whose previous government had negotiated a 130 billion-euro bailout package that had private lenders taking, in some cases, up to a 75% hit to the value of their debt holdings, appears to be in complete turmoil once again. The pro-austerity conservative parties, New Democracy and Pasok, lost a significant amount of their support as the electorate voted in left-wing, anti-austerity party members. With no clear majority in the Greek parliament, the probability of forming a functional (key word there) government just dropped by a lot.

So where does this leave us?
Negotiations in Europe have moved at a pace that makes molasses in winter look like Speedy Gonzalez. The possibility that France could back out of future debt negotiations with Spain's debt problem looming large isn't going to sit well with investors around the world.

As for Greece, the problem may not seem as immediate, since its government has been largely dysfunctional from the beginning of this debt crisis, but it may make implementing already agreed-upon austerity measures even tougher. I would overwhelmingly say these elections are bad news for U.S. investors who favor certainty as opposed to change.

What does this mean for your money?
With many investors trading more on emotion than actual earnings results, it's likely we can expect more pressure on European-based businesses. The fallout in some companies can be, at least to some extent, justified as with large Spanish banks, Banco Santander (NYSE: STD) and Banco Bilbao Vizcaya Argentaria (NYSE: BBVA). Both of these institutions are dealing with ridiculously high unemployment rates and commercial real estate portfolios littered with potential problem loans.

But we're also likely to see pressure on companies that won't be directly affected by austerity. Two such companies that may get lumped into the "guilty by association crowd" are France Telecom (NYSE: FTE) and U.K.-based oil services company BP (NYSE: BP).

France Telecom has been on a steady downtrend over concerns that its mobile business may suffer as Europeans cut back on discretionary spending. What investors are failing to take notice of is France Telecom's strong international growth in Sub-Saharan Africa and even in troubled Spain.

As for BP, weakness in the stock makes little sense because so many of its oil assets are diversified throughout the world. There may be some give and take as emotional oil traders react to the unpleasant news out of Europe, but that's hardly a game-changer for a company that's putting its Gulf of Mexico PR nightmare in the rearview mirror.

United they stand, divided they ____?
It's tough to say whether the eurozone as a whole is headed into recession, but I can't figure that the mixed results in the elections this weekend helped that cause. I've postulated before that prolonged recessions seem inevitable in Greece and Spain, and austerity measures designed to curb rapidly rising debt levels in France and Germany are likely to curb any economic strength. In short, the possibility of a Euro-recession is a real possibility.

The secret to survival over the next few months, until we get a better understanding of how these new governments will cooperate with one another, is to focus on strong cash flow businesses that tend to perform well even in stagnant times. This means telecom and health-care companies just might be your best shot at betting on a European recovery.

Disagree with me? Tell me about it in the comments section below.

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This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.