One is how to ensure budget discipline over spendthrifts and the other is how to improve competitiveness so that the gap between the zone's richer north and poorer south is narrowed. The proposals will feed into work by EU president Herman Van Rompuy.
"The markets will be taking a very close look on August 16," said a French trader. "[Sarkozy and Merkel] have to send a signal that things are moving forward. That will be very important."
But the discussions are taking place against a darkening backdrop.
Economic turbulence and growing reluctance for self-sacrifice make ambitious proposals look unlikely.
In Germany, a growing number of legislators in the governing centre-right coalition are agreeing vocally with a public worried that their country - the EU's paymaster - is being led by the nose.
France and Italy are calling for national debt in the euro-zone to be integrated with the launch of a single "euro-bond". By pooling their strengths, according to this argument, economies could calm the frenzy in national bond markets and demolish the speculators who are gunning down one weak economy after another.
But Germany, the wealthiest economy, sees things differently. By underwriting a debt for all, but without having political control over how it is spent, Germany would be handing a blank cheque for the freeloaders, say critics.
Finance Minister Wolfgang Schaeuble spoke of enhancing "stability pact" rules in the eurozone that are supposed - but so far failed wretchedly - to punish budget over-spenders.
Merkel's coalition partners, the pro-business Free Democrats, have taken an even stronger line. Their parliamentary leader Rainer Bruederle warned implicitly at the weekend that the party would not approve the July 22 bailout and EFSF scheme unless countries inscribe debt ceilings into their constitutions as a matter of law, as Germany does.
Economically, too, the room for generosity is narrowing fast. After Greece, Ireland, Portugal, Spain and Italy, it is now the turn of mighty France to be targeted by sellers. Rumours swept the markets last week that, like the United States, it would lose its coveted AAA credit rating, given its poor growth, large budget deficit and deepening commitment to the euro bailout.
Italy last week unveiled a €45.5 billion austerity budget aimed at bringing down its public deficit to below 3 per cent of gross domestic product (GDP) by 2013, as stipulated in the July 22 summit.
Sarkozy will meet on Thursday with his top advisers to see how France can slash its deficit from 7.1 per cent of GDP last year to 3.0 per cent, the eurozone ceiling, by 2013.
But growth figures last week have punched a hole in expectations for tax revenue. The Government is assuming the economy will expand by 2 per cent this year but there was no growth at all in the second quarter. Journal du Dimanche says the Finance Ministry is looking at cobbling together a revenue-raising package of "around €10 billion" for 2012. But, with an eye on next May's presidential elections, there will be no increase in income tax or VAT, nor cuts in welfare.
Economist Jennifer McKeown said: "It will be extremely difficult to implement the aggressive austerity measures that are needed to convince markets that the government finances are on a stable footing."
