Italy has granted 20,000 Tunisians temporary residence permits, allowing them free travel in the passport-free Schengen zone of 25 countries.
Last week the French temporarily halted trains with migrants at the Italian frontier, causing an international incident.
The BBC reports an unnamed top official at the presidential palace in Paris said: "The governance of Schengen is failing. It seems there is a need to reflect on a mechanism that will allow a temporary suspension of the agreement, in case of a systemic failure of an external (EU) border."
Suspension of the agreement is allowed under the 1985 Schengen Pact only for a "grave threat to the public order or internal security" and only for 30 days.
French President Nicolas Sarkozy is expected to raise the issue with Italian Prime Minister Silvio Berlusconi when he visits Rome Tuesday.
Italy and France are patrolling the Mediterranean by sea and air in an attempt to stem the refugee flow from Tunisia, Egypt and Libya.