The French draft, circulated in the Security Council on Friday, proposes to "recognise that the parties concerned have made significant and noticeable progress towards implementing some of the provisions of Resolution 1559", which called for the withdrawal of foreign forces from Lebanon.
Syria declared an end to its 29-year troop presence in Lebanon on Tuesday.
The text proposes to "deplore the fact that there has been no progress towards the disarmament of Lebanese and non-Lebanese militia, and that the government of Lebanon still does not fully exert control over all its territory."
Resolution 1559 calls for the disarmament of all militias, in reference to the Shia movement Hizb Allah and Palestinian factions.
The French text proposes to "welcome the deployment of Lebanese Armed Forces to positions vacated by Syrian forces ... and call for the deployment of additional Lebanese Armed Forces throughout the South of Lebanon."
The text could be passed as a UN Security Council resolution or a presidential declaration after debate and possible amendments, diplomatic sources said.
The text was proposed as a reaction to a UN report released after Syria declared its withdrawal. In the report, UN Secretary-General Kofi Annan said the claim would be tested by a team of military experts who were sent to Damascus.
On Friday, Annan said that "obviously there's visible progress" in Syria's withdrawal from Lebanon but that he would wait for his team's report before making a final judgment.
The French text asks for the "full cooperation" of Syria and Lebanon with the UN experts.
UN resolution 1559 calls for
Hizb Allah to disarm
A US diplomat, Stuart Holliday, said Washington remained "concerned about reports of continuing Syrian involvement and interference in Lebanese internal affairs".
"Of course, we continue as we did in the resolution to call for the disbanding of all militias in Lebanon. There is no role for armed militias in Lebanon, for Hizb Allah as the Lebanese people seek to build a more hopeful and democratic future," he said.
Lebanon will start legislative elections on 29 May.