David Cameron and French president Francois Hollande have agreed that the draft proposals for reforming Britain's membership of the EU provide a "firm basis" to agree a deal this week, Downing Street has said.
The hastily arranged meeting with Mr Hollande came ahead of a crunch Brussels summit at which the Prime Minister hopes to sign up EU leaders to the reforms so he can hold an in/out referendum in June.
Downing Street's assertion suggests French concerns over financial protections for non-eurozone states and special treatment for the City of London have been calmed.
A Number 10 spokesman said: "The Prime Minister and President Hollande had constructive discussions on both the UK renegotiation and Syria in Paris this evening.
"They agreed that we are making good progress on the UK renegotiation and that the draft text from the European Council provides a firm basis to reach agreement at this week's summit."
Mr Cameron will now travel to Brussels for talks with selected MEPs on Tuesday amid Eurosceptic warnings that the European Parliament could veto aspects of the deal after the referendum.
MEPs will eventually have to approve parts of the reform package including restrictions on EU citizens' benefits but Downing Street has insisted any deal would be a "legally binding document under international law, entered into by the 28 leaders of member states" and that the European Parliament should deliver on that.
Mr Cameron had been expected to meet the heads of all the groupings in the European Parliament but was branded a "chicken" by Nigel Farage after Number 10 revealed the PM will not meet the Ukip leader.
Instead he will meet European Parliament president Martin Schulz, leaders of the centre-right EPP and the Socialist grouping, and three MEPs who have been acting as "sherpas" in the negotiations.
Meanwhile, European Council president Donald Tusk warned that Mr Cameron's renegotiation was "very fragile" and unless handled carefully could lead to the break-up of the union
Mr Tusk said it was a "critical moment" as he told EU leaders to start listening to each other's concerns because "what is broken cannot be mended" and the "risk of break-up is very real".
Mr Tusk is undertaking a whirlwind tour of EU capitals including Berlin, Paris and Athens to sell the package of reforms he drafted in response to Mr Cameron's demand for change.
Britain's renegotiation is the first item on the agenda for the two-day European Council summit in Brussels beginning on Thursday.
However, the gathering of 28 EU leaders is not scheduled to conclude until Friday lunchtime, after which Mr Cameron will call an immediate Cabinet meeting if he secures a deal.
That will effectively fire the starting gun on the referendum battle, as Eurosceptic ministers will be given the green light to campaign for a Leave vote in the poll expected on June 23.
Mr Cameron had come under pressure from ministers to bring Cabinet forward as Eurosceptics feared the Remain campaign would have an advantage if collective responsibility was not suspended until the next scheduled meeting of the PM's top team on February 23.
They believed the Remain campaign would steal a march in the vital first few days of the campaign by leaving the PM free to proclaim the merits of the deal in weekend TV interviews and a statement to the Commons on Monday, while colleagues remained gagged.
While the likes of Iain Duncan Smith, Chris Grayling and Theresa Villiers will be expected to join the Leave campaign, all eyes will be on waverers such as Theresa May and Boris Johnson to see which side they back.
Agreement this week remains far from certain, with Downing Street confirming that key details still need to be "pinned down".
Mr Cameron has made it clear he is ready to wait until the next summit in March to try again for a deal, rather than accept one that falls short of his demands.
If the summit runs over into Friday evening or Saturday, the PM will review whether to call ministers to Number 10 for a weekend Cabinet meeting.