European Union leaders are seeking a way to bounce back from Sunday's landmark elections that saw a partly hostile and largely apathetic public question their project of closer cooperation as never before.

The parties of leaders like French President Francois Hollande and British Prime Minister David Cameron were shaken to the core by anti-EU challengers, yet they have offered starkly different alternatives on how to deal with the situation ahead of Tuesday's EU summit.

Hollande has said that "France's future is in Europe" and has remained steadfast in the defense of joint policies and common stands. Cameron will increase his calls for drastic reforms to pull powers back from Brussels and give individual member states more breathing space to set their own policies.