Sarkozy, who has pushed legislation that institutes tests of language and fundamental French values, pressed home his argument that immigration needs to be controlled. "If we do not have the courage to master migratory flows, we will not succeed with integration," he said.
"Our countries are open; they are not closed, they are not fortresses," he said. "But anyone who asks to come must respect the culture he wants to become his own."
On the diplomatic front, both countries are involved in efforts to address concerns over Iran's nuclear program. Both leaders have discussed the issue with U.S. President George W. Bush in separate visits to the United States over recent days.
Sarkozy spoke in the U.S. state of Virginia of "the need to toughen" U.N. sanctions in place against Tehran over its defiance of demands to halt uranium enrichment, which could be used both to generate nuclear power and create the fissile core of warheads.
At Bush's ranch in Texas, Merkel made clear that Germany will back more sanctions if Iran fails to give way and stressed that she and Bush agree that the issue "can be resolved diplomatically."
She also said that "the signals, if developments continue to be so negative, point to us limiting our trade activities" with Iran, and that she would "remain in contact with German business" on that.
In a weekend video message, Merkel said that Monday's meeting with Sarkozy also would address "economic problems," but she did not offer details. France has expressed concern over the euro's rise against the U.S. dollar, while Germany has sounded more relaxed.