he Paris talks came ahead of a crucial meeting of European leaders next week about the future shape of the EU.
Mr Sarkozy has said a new treaty is needed to impose financial discipline on countries using the single currency.
But Mr Cameron said steps could be taken to shore up the euro and improve the competitiveness of its weaker economies without treaty change.
Britain is not in the eurozone but is concerned a reorganisation could marginalise its influence in the EU.
The two leaders discussed plans to reorganise the governance of the eurozone, which will see closer co-operation within the 17-strong bloc, potentially reducing Britain's influence.
The move will be considered by the European Council at the end of next week, but Germany and France will agree a plan of action on Monday.
Any reforms of the Maastricht Treaty rules governing the eurozone will have to be agreed by all 27 members of the European Union.
'Grappling'
Mr Cameron said they had enjoyed "a very good meeting" and Britain wanted "to help solve the crisis in the eurozone".
"In the end, what that is about is convincing the markets that the institutions of the eurozone will defend and promote and protect the currency with everything they've got," he said.
"It also means fundamentally grappling with the lack of competitiveness of some European economies."He added: "Neither of those things actually require treaty change. but I'm very clear if there is treaty change I will make sure that we further and protect Britain's interests."
Mr Cameron has previously vowed to use any wider treaty change as an opportunity to claw back some powers from Brussels to Westminster.
BBC correspondent Christian Fraser says Mr Cameron is under pressure from Conservative backbenchers and will seek to explore what Britain might get in return for its support.
But the next few days are critical to the survival of the single currency, and our correspondent says it is unlikely Mr Cameron will want to slow down agreed eurozone changes.
Asked about the talks, Chancellor George Osborne said that although the UK did not want to be part of any future integration, it was in the UK's "economic interest" that eurozone countries worked more closely together "to sort themselves out".
On Thursday, Bank of England governor Mervyn King said the Bank was making unspecified "contingency plans" in case of a eurozone break-up, and that banks should brace themselves to withstand the "extraordinarily serious and threatening" economic situation.
In a speech on Thursday, Mr Sarkozy said France and Germany must come together to stabilise the eurozone and safeguard the euro's future.
'National interest'
Mr Sarkozy and German Chancellor Angela Merkel are due to meet on Monday to propose measures to "guarantee the future of Europe", Mr Sarkozy said.
Downing Street said it was waiting to see the options paper for reform which European Council president Herman van Rompuy is drawing up for next week's gathering of EU heads.But Conservative MP Bill Cash - one of the party's most longstanding Eurosceptics - said any move to closer fiscal integration among eurozone members would "undermine" the UK, as the government would be regularly outvoted on key issues.
"We are witnessing the creation of a kind of German zone driven very much by the needs of Germany and France and not in the interests of the UK," he told the BBC News Channel.
And the UK Independence Party, which campaigns for the UK to leave the EU, said Mr Cameron was being "softened up" as part of a process that would inevitably lead to closer political union.
"The crisis in Europe provides a once-in-a-lifetime opportunity for the British prime minister to act in British interests," its leader Nigel Farage said.
"That he refuses suggests that he prefers the polite applause of Paris, Berlin and Brussels to the wishes of the British people."
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