Here is a look at some of the stories that CNN plans to follow this week:

Will elections shift Europe's debt crisis response?

Keep an eye on how stock markets react this week as investors digest the results of two key elections in France and Greece that might signal changes in how Europe handles its 3-year-old debt crisis.

With Francois Hollande defeating incumbent Nicolas Sarkozy in today's French presidential runoff, questions will be raised about whether France will continue to commit to the kind of spending cutbacks that other European nations have deployed to battle the debt crisis. Hollande campaigned on the need to focus more on economic growth to reduce public debt, as opposed to austerity, CNNMoney's Hibah Yousuf reports.

Meanwhile, Sunday's parliamentary elections in Greece will help shape a ruling coalition that could affect the course of austerity measures there – measures that outside lenders had imposed in return for keeping the nation's finances somewhat afloat and ensuring Greece could keep the continent's common currency, the euro. The austerity measures have led to cuts in jobs, wages, pensions and benefits, and some parties were gaining traction with anti-austerity messages.

GOP's most senior U.S. senator on the ropes

The political future of the U.S. Senate's most senior Republican will be on the line Tuesday when Indiana votes in a GOP primary.

A poll released last week showed Sen. Dick Lugar 10 percentage points behind challenger Richard Mourdock, Indiana's state treasurer. Lugar, 80, is seeking his seventh six-year term, but in this election cycle he has been forced to defend his residency in the state, as well as his conservative bona fides as the tea party and other groups have proclaimed Lugar to be too moderate and too willing to work with Democrats.

The race has drawn the attention of high-profile political figures, with Mourdock getting endorsements from former GOP presidential candidate Rick Santorum, U.S. Rep. Michele Bachmann of Minnesota and former Alaska Gov. Sarah Palin. Lugar has been backed by the U.S. Chamber of Commerce, U.S. Sen. John McCain of Arizona, Indiana Gov. Mitch Daniels and pop singer Pat Boone.

Student loan battle goes to Senate

The latest chapter in a battle over whether and how to keep federal student loan rates from doubling in July is expected to unfold in the Democratic-controlled U.S. Senate this week.

The Senate is expected to consider a Democratic-pushed proposal to extend the current 3.4% interest rate. Senate Democrats have said they want to make up for the $6 billion cost by ending some tax loopholes for corporations, a move opposed by Republicans.

The Republican-controlled House last month passed a bill that would extend the lower rate for a year, but it would cover the cost by dipping into a health care fund intended to promote wellness, prevent disease and protect against public health emergencies. The fund is part of the 2010 Affordable Care Act detested by Republicans.

President Barack Obama has threatened to veto the House version. After the Senate passes its bill, the two chambers are expected to try to negotiate a compromise version.

Annan to brief U.N. on Syria

Days after a chief U.N. peacekeeper said the Syrian government and opposition forces are violating a cease-fire, U.N. special envoy Kofi Annan is expected to brief the U.N. Security Council on the status of his peace plan Tuesday.

The cease-fire negotiated by Annan was supposed to go into effect April 12, but deadly attacks attributed to both sides have escalated doubts that the 14-month uprising can be resolved. The United Nations estimates that at least 9,000 people have died in the conflict but that estimate is old and believed low by opposition groups.

On Monday, Syria is scheduled to hold parliamentary elections for 250 seats, state media said. The election comes after the nation adopted a new constitution that is said to allow political parties to compete with the ruling Baath Party.

Sentencing scheduled after failed 'stand your ground' defense

A woman whose lawyer unsuccessfully argued that Florida's "stand your ground" self-defense law exonerates her in a 2010 incident in which she fired a bullet into a ceiling is scheduled to be sentenced to prison on Friday.

Marissa Alexander is expected to receive a mandatory 20-year sentence after being found guilty of three counts of aggravated assault. She claims she fired a warning shot that hit no one during a quarrel with her husband, and her attorneys unsuccessfully used the "stand your ground" law as a defense. The law has been under scrutiny since an incident not connected to the Alexander case: the February shooting of teenager Trayvon Martin.

Fortune 500 announced

Fortune magazine will release on Monday its annual list of the 500 largest companies in the United States. The Fortune 500 are ranked according to revenue, not other measures such as profits or market capitalization. The top five on the magazine's 2011 list were, in order, Wal-Mart Stores, Exxon Mobil, Chevron, ConocoPhillips and Fannie Mae. A lot has happened in the economy in the past year, so the top 10 could change; the full list changes every year.