Editor's note: An earlier version of this article referred to Telefonica's 10% dividend yield. However, Telefonica actually suspended its dividend in July. The article has been amended. We regret the error.

LONDON -- I think I'm getting bailout fatigue. The eurozone has had so many bailouts I've lost count. There have been bailouts of Greece, bailouts of Portugal, bailouts of Ireland, bailouts of banks, and bailouts of bailouts (or did I make that last one up?).

It's not just me that is getting fed up -- the markets, too, are getting sick of the constant eurozone machinations. At some point you have to think: "What the heck, let's just get on with investing."

The fact is that the eurozone troubles have meant that European shares have been bid down to dirt-cheap levels. For the contrarians among you, perhaps it is finally time to take the plunge and buy into Europe.

And if there is, at long last, a robust eurozone recovery, you could really stand to profit.

So I thought I'd take a look at some of the prime bargains in Europe's markets. In particular, as a holder of Vodafone shares, I thought I'd analyze what Europe has to offer in terms of telecom companies.

Telefonica: a company of two halves
Let's start with Spain's telecom champion, Telefonica (NYSE: TEF). This an international telecom firm with businesses in 20 countries stretched across Europe and North and South America. We in the U.K. will know it as the owner of O2, Britain's biggest mobile operator.

But it also has large operations in Spain, Germany, Brazil, Columbia, Argentina, and Peru, spread across mobile, fixed-line telecoms and broadband.

Despite all these credentials, Telefonica has in recent years been something of a falling knife, with the share price halving since the beginning of 2011. Why?

Well, I see Telefonica as a company of two halves. Group profit halved in 2012, as the company was hit by reduced profitability and substantial restructuring charges in Europe, particularly in its home market of Spain. The group's dividend was suspended as a result.

But, on the other hand, Telefonica is also a play on emerging market growth, with sales in Latin America growing by 13.5% in the past year. The region now makes up half of the business' profits. Furthermore, the European troubles might be temporary as Telefonica has pledged to restart its dividends at 0.75 euros per share during 2013.

This is clearly a company in transition, but I feel that the pain in Europe will eventually lessen, while the Latin American business will continue to grow, and will soon dominate the company.

All told, at the current price of 10.06 euros and on a trailing price-to-earnings ratio of 10, I'm happy to just keep an eye on Telefonica for now. If the group's promise to reintroduce a 0.75-euro-per-share dividend comes good, the resulting 7%-plus yield may well be worth owning.

France Telecom: just look at that dividend
France Telecom
(NYSE: FTE) is the world's second-largest telco, with some 180,000 employees and 193 million customers. It has operations around the world, most of them under the Orange brand.

The company's share price has been falling as eurozone sentiment has waned. However, unlike Telefonica, France Telecom has displayed remarkable stability despite Europe's troubles, with operating income largely unchanged over the past three years.

What's more, the price fall has made the shares enticingly cheap. It is on a P/E ratio of 7, but the main attraction is the dividend yield, which is an incredible 13%. Whatever language you speak, that yield screams "Buy me!" to income investors.

Deutsche Telekom: a steady performer
So what about Germany's major telecoms company, Deutsche Telekom (NYSE: DT)? Like its Spanish and French peers, it provides a blend of mobile, fixed-line telecoms, and broadband services, under its T-Mobile/T-Online/T-Home brands.

I see Deutsche Telekom as rather like France Telecom: a steady but unspectacular performer with neither the highs nor the lows of Telefonica.

But whereas France Telecom has, in my view, been heavily oversold, Deutsche Telekom is not nearly so cheap. At its current share price of 9.50 pounds, based on its results for the first half of 2012, I estimate the company is on a P/E ratio of about 14, with a dividend yield of just over 5%. That's perfectly respectable, yes, but not the stonking buy I was hoping for.

Foolish bottom line
Turn your eyes away from the apocalyptic headlines, dig deeper into Europe's stock markets, and you can really unearth some bargains.

Whisper it quietly, but I think that, after so much pain, Europe is gradually starting to heal. Buying into France Telecom could result in you gaining big time if Europe really does recover. And, even if it stays in the doldrums, those mega dividends should ensure that you still profit.

I think the telecoms sector is a great one to invest in. What other sectors does The Motley Fool recommend buying into? To find out, click on the link to read our free report: "Three Top Sectors For 2012".

More investment opportunities from The Motley Fool:

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.