Read More European bonds signaling trouble?
The polls open on Thursday and a result is expected before markets open Monday morning. At stake are 751 seats at the European Union (EU)'s Parliament, which forms part of its legislative arm.
With the financial transaction tax, the banking union and deposit and market regulations still on the agenda, market participators are keen for the status quo to be maintained, to decrease uncertainty.
However, fringe politics and anti-EU parties have grown in strength in the five years since the last election and Greece's fragile coalition is seen vulnerable, with snap national elections a possibility.
"If the protest vote results in governments backing away from austerity and reform, then we could see outflows from both euro zone bonds and stock markets, plus a resumption of the risk premium in the euro," Marshall Gittle, a market strategist at IronFX said in a note.
However, there is a potential savior in the shape of European Central Bank (ECB) action on the horizon. ECB President Mario Draghi is expected to announce fresh policy action on June 5 to see off deflation, in what could be his most closely watched press conference since his "whatever it takes" speech in 2012.
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"The positive liquidity outlook should have a numbing effect on the market in relation to concern on political risk," analysts at Rabobank said in a note Wednesday. "Therefore we continue to consider entering a spread narrowing position."
One problem is that another rate cut, or even the instigation of negative rates on deposits, might disappoint markets. Many investors are hungry for a Federal Reserve-style quantitative easing (QE) program. Anything short of that could take the wind out of bond markets, given hopes of large asset purchases that would bring down yields.
Jon Jonsson, managing director at Neuberger Berman, believes that last week's correction was due to investor over-excitement about the possibility of QE. He explained that he was shorting some European government bonds because they were overpriced.
"I'm actually short Germany in the 10-year," Jonsson said. "It's a great short...I actually think a lot of the government markets are overbought at this point."
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Trader chatter last week focused on whether last week's European selloff could lead to more caution in other fixed-income markets. The U.S. 10-year Treasury market reacted to the selloff and the European corporate market saw some softening.
Nonetheless Peter Chatwell, an interest rate strategist at Credit Agricole, said that bond yields on the two sides of the Atlantic could yet move in different directions.
"(The) impact on U.S. Treasurys should be limited, as the U.S. economy continues to diverge from Europe, so we may simply find the U.S. Treasury-Bund spread explores new territory," he told CNBC via email.