That followed Standard & Poor's revision of France's AA outlook to negative from stable last week.
German 10-year Bund yields, which set the standard for borrowing costs in the euro zone, hit a record low of 0.824 percent, 2 basis points lower on the day.
"Given the already very low yield level, Bunds are likely to find it increasingly difficult to advance further," said Manfred Bucher, senior analyst at Bayerische Landesbank. "However, they remain well supported amid increasing skepticism on the economy and deflation concerns."
Read MoreGerman investor morale tumbles as contraction looms
France's 10-year yields also fell to 1.18 percent, with the ratings move not hurting the appeal of its debt as markets are focused more on the impact a weakening outlook would have on central bank policy.
The euro five-year, five-year breakeven forward, which shows where markets expect 2024 inflation forecasts to be in 2019 was around 1.76 percent, a record low. It has fallen 20 bps in the past month.
Annual inflation in the euro zone slowed to just 0.3 percent in September and oil prices around four-year lows are stoking fears the euro zone could fall into deflation, which could cripple economic growth even more.
Read MoreGreek bond yields pass 7% as worries return
"With deflation worries still very much to the fore in the euro area and the pressure on the ECB to take further action in coming months, Bunds will remain underpinned in the near term," said Nick Stamenkovic, bond strategist at RIA Capital Markets.
Greece was the only market in the euro zone which ignored prospects of ECB easing. Ten-year yields rose 55 basis points to 7.60 percent, their highest since March.
Investors fear that an early exit from the bailout program would derail Athens' fragile fiscal progress and that snap elections are inevitable next year when a presidential vote is held. That brings the prospect of a political deadlock or a government led by the radical leftist Syriza party, which has campaigned against austerity.
"Investors are worried that Greece cannot survive alone," ING's Giansanti said.