UPDATE 1-In Paris, Merkel and Macron seek common ground on euro zone reform

* Merkel's first foreign trip since re-elected as chancellor

* Macron, Merkel both keen for euro zone reform

* Differences persist over how far to go (Updates with quotes from Merkel and Macron ahead of talks)

PARIS, March 16 (Reuters) - President Emmanuel Macron and German Chancellor Angela Merkel pledged on Friday to formulate a roadmap for euro zone reform by June, but they may struggle to find common ground on further change in Europe.

Merkel, who was narrowly re-elected to a fourth term as chancellor, wants to fulfill her incoming government's pledge to deliver a "new start" for Europe. Macron, too, has made euro zone overhaul a central goal since taking power last May.

"We are not always on the same page. But Germany and France have also achieved a lot in the past and now we have the firm intention to do that again," Merkel said before her meeting with Macron, their first since she formed a new coalition government.

Merkel said the goal of the reform push had to be to stabilize the euro zone and improve the competitiveness of the single currency bloc.

"We'll put forward a clear, ambitious roadmap by June for this overhaul," Macron said. In addition to the future of the euro, the roadmap should also address further integration of the bloc on migration, defense and trade, he said.

Merkel also said there was a need for more convergence on asylum policies.

There is already substantial reform under way in the euro zone, including the creation of a banking union among its 19 member states and plans for a single deposit insurance scheme that would protect individuals' savings.

However, the appetite for deeper integration, such as Macron's grand ideas for a standalone euro zone budget, a single euro zone finance minister and a dedicated fund that would help countries facing external shocks, is limited.

Members of Merkel's conservative bloc are wary of more comprehensive European integration, especially if it means that Germany, Europe's economic powerhouse, would be pooling risks and debts with other, less financially stable countries.

The Netherlands and seven other EU states issued a joint statement in early March saying a lot had already been done to strengthen the architecture underpinning Europe's economic and monetary union, and the first priority should be to ensure countries implement those measures.

Macron has said his plans are for the long-term and will be the natural outcome of deeper euro zone integration. But that raises the question of what France and Germany - often referred to as the engines of the EU - can come up with in the short-term to show they are delivering on a fortified European project.

Macron, 40, has waited impatiently for the Germans to form a government and is itching to press ahead.

The chancellor, 63, knows that Macron, in his first term, needs to deliver on his promises, well aware that a large proportion of France's electorate remains susceptible to far-right and far-left populists who are skeptical about the EU.

In January, when they last met for formal discussions on the eurozone and Merkel was still negotiating over a coalition, the pair said they hoped to present their plans to member states at an EU summit in March.

But that gathering is a week away and it appears unlikely that they will have anything concrete to put forward by then, with the next EU leaders' meeting in June now the new deadline.

"We must agree by June a Franco-German roadmap for the whole euro zone. It'll be very tough work," French Finance Minister Bruno Le Maire said after talks with his German counterpart, Olaf Scholz.

Yet, even if they can get the 17 other euro zone members to agree to further reforms -- how better to deploy their 500 billion euro ESM rescue fund -- there will be a tight schedule to implement those changes before the EU has to tackle its next big challenges: Britain's formal exit from the union in March 2019 and European Parliament elections shortly afterwards. (Additional reporting by Ingrid Melander in Paris and Joseph Nasr in Berlin Writing by Luke Baker Editing by Richard Lough and Raissa Kasolowsky)