Assad is "stoking injustice, disorder and extremism" in Syria, British Foreign Secretary Philip Hammond and his French counterpart Laurent Fabius wrote in a joint editorial published by newspapers Le Monde and Al-Hayat.
They claimed that Assad is seeking to rehabilitate his public image despite a conflict in Syria which has lasted nearly four years, killed at least 210,000 people and displaced nearly 12 million others.
"For our own national security, we have to defeat ISIL (IS) in Syria. We need a partner in Syria to work with against the extremists and this means a political settlement agreed between the Syrian parties leading to a unity government in Syria," the editorial said.
One of a group of French lawmakers who met Assad in Damascus on a much-criticised private trip said Friday that the Syrian leader "expected to no longer remain isolated in the face of the terrorist threat".
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That visit has been strongly condemned by French President Francois Hollande and Prime Minister Manuel Valls.
The editorial added that most Syrians would not accept Assad as part of the solution to the conflict.
"Proposing Assad as a solution to the extremists is to misunderstand the causes of the extremism," it said.
UN peace envoy Staffan de Mistura is travelling to Syria tomorrow to hold talks on a plan to halt fighting in the key northern city of Aleppo.
He told the UN Security Council last week that the Syrian regime was willing to suspend air raids for six weeks in Aleppo, which is divided into regime and rebel-held areas.