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On his European tour President Obama comes to France. He will be well received. He remains a popular figure in Europe, as has been demonstrated in London.

There can never be a return to the ecstatic reception Obama received in the Tiergarten in Berlin when he was only a candidate. Europe then betrayed its yearning for an idealistic US leader who sounded a different note to George W Bush.

In his first two years in office President Obama has, at times, seemed almost cowed by the Bush legacy. He has been a reluctant interventionist. In moments of crisis America, in his view, should not always be the indispensable power. He has no longer set out to impose America's brand of democracy in troubled corners of the world. All of that has sat comfortably with most Europeans.

Over Libya, however, some Europeans accused President Obama of dithering. Some in Washington let slip their frustration and wondered whether Europe would prefer a return of the president from Texas. In the event Washington came around to supporting the use of military power in Libya to protect civilians, as urged by David Cameron and Nicolas Sarkozy.

But Obama was clear. The Americans would play a support role. The lead would be taken by the Europeans - which meant Britain and France. It sent a powerful message to Europe. Libya was their backyard. There was was no obvious American interest in Libya beyond preventing a massacre of civilians.

The message, not yet fully digested in Europeans capitals, is that in future their forces will have to do more - just at a time when military budgets are being slashed.

President Obama accepted yesterday the Libyan operation had its "limitations", but insisted there would be "no let-up on Gaddafi". The Americans believe that over time support for the Libyan leader will collapse, but the larger part of the campaign will be left to the Europeans.

What the American president will do, while attending the G8, is to seek ways to bolster the fledging democracies in Tunisia and Egypt. The IMF and the World Bank will give their assessments of what is needed to modernise and stabilise those countries.

Obama wants long-term investment and a commitment to boost trade. The EU - always more confident with soft power - is already committed to investing in Tunisia and Egypt and eventually Libya. But Europe's generosity has its limits at a time of low growth and austerity. But America and Europe see eye-to-eye in understanding that, at this time, they have to invest in the Arab Spring.

Europe, like America, is fearful of its waning power in the world. President Obama addressed that fear directly in London. He spoke of the rise of countries like China and India and the concern that this would be accompanied by the "decline of American and European influence around the world". He went on to say "perhaps, the argument goes, these nations represent the future, and the time for our leadership has passed.

"That argument is wrong. The time for our leadership is now."

It is a theme that he will return to on the campaign trail. No American candidate has prospered by pointing out American limitations.

Europe's problem is that the EU pines for influence on the world stage but influence comes with economic power - and Europe has not yet found the way to adjust to the challenge from emerging economies.

On the Middle East, President Obama is much closer to the Europeans. His recent speech, in which he argued that a future Palestinian state should be based on territorial lines that existed before the 1967 war - although with exchanges of land - is supported by many European governments.

Europe and America are agreed on Israel and Palestine living side-by-side in security and peace. President Obama says he is confident such a solution can be found. But the obstacles are immense.

Only this week the Israeli Prime Minister told Congress that there would be no return to pre-1967 borders. He was widely applauded. In an American election year Israel will surely use its influence.

The Palestinians say that if there are no peace talks by September they'll go to the UN to seek statehood. Some European states will support this. President Obama is clear that such a route for the Palestinians would be a mistake. There may be tension here between Washington and the European capitals.

Whether it be over Afghanistan or Iran there are no great rifts between Europe and America. All leaders know that the events in North Africa and the Middle East present a once-in-a-generation opportunity to support democracy. That is the challenge.

When President Obama sided with the protesters in Tahrir Square in Egypt against President Mubarak, an old American ally, he sided with those hungry for change and freedom.

The outcome of those upheavals remains very uncertain.

The Americans and the Europeans see the challenge, but the question is whether at a time of economic weakness they have both the means and the will to make a difference.