Both have created problems for themselves that cast lengthening shadows on their political future. Merkel, safely entrenched and still popular despite decisions that have piled new tax burdens on her German electorate, is facing a major challenge to her future from former Finance Minister Peer Steinbrueck.
The newly chosen leadership candidate for the opposition Social Democrats wants Merkel out and seems not at all fazed by her continuing support base in Germany's conservative Christian Democrats and coalition partners Free Democrats.
Steinbrueck, 65, served as finance minister from 2005-09 when the SPD was a junior partner in a previous coalition.
His rise within the SPD and the potential to face Merkel in next year's election was rated by German analysts as the most dangerous development for the chancellor because of Steinbrueck's perceived appeal to the middle-of-the-road road Germans.
Steinbrueck also seems confident he can eject Merkel but keep her Green partners to form a new coalition, in about the same way the Greens aligned with the SPD in the past.
"We want to remove this government. We want to replace it with a Red-Green government," Steinbrueck told a news briefing.
SPD strategists are already at work, having persuaded both party leader Sigmar Gabriel and former Foreign Minister Frank-Walter Steinmeier to make way for Steinbrueck.
Although SPD pledges to clean up the markets and prevent what it calls Merkel's excesses, the party has yet to endear itself to the broad conservative support behind Merkel, but that could change.
German patience with eurozone troubles is running thin and Germans remain anxious over hints from Spain that it may need up to $76 billion to shore up its banks. Merkel's response to Spain's woes could affect her own approval ratings in Germany.
Meanwhile, Hollande has won enemies across the board with a controversial plan that aims to stimulate the French economy with funds gouged out of the country's super rich, higher taxes on the not-so-rich and what critics see as little change in the government's spending plans.
French Prime Minister Jean-Marc Ayrault said a new 75 percent tax rate would target people earning more than 1 million euros -- $1.3 million a year.
Critics say the higher taxes won't help French recovery but more spending cuts might. The government hopes to raise through taxes about double what it promises to cut in spending -- $26 billion against about $13 billion of cuts.
Hollande won election on a promise to shun austerity -- in direct contrast to the rest of the eurozone -- and aim for higher growth. What many French citizens didn't anticipate was a regime of punishing taxation to fund the growth.
Critics say the higher taxes are a certainty but the same cannot be said of the promised growth and recovery. Hollande's strategy has been compared to a huge gamble, with a question mark on his own political future.