That rebound coincides with improved economic data and signals from major central banks that they are on pause for now.
The leaders of France and Germany agreed last month on a proposal for such a budget that would be used to smooth out economic difference between euro zone countries.
Euro zone economic growth will slow this year and next from a peak expansion in 2017, the European Commission forecast on Thursday.
The dollar index gained 0.34 percent, with the euro down 0.27 percent to $1.2198. The Japanese yen firmed 0.55 percent versus the greenback at 106.73 per dollar.
Euro zone businesses started 2018 by increasing activity faster than at any time in well over a decade as new orders surged.
Euro zone private businesses ended the third quarter growing much more strongly than predicted.
Macron on Thursday backed Germany's idea of a European Monetary Fund (EMF) but stressed the ultimate goal should remain a euro zone budget.
Global investors raised their euro zone equity exposure to the highest level in at least five years in August.
Schulz called on Thursday for accelerated reforms to the euro zone, and the basis of a strengthened currency union to be agreed by Britain's Brexit in 2019.
Euro zone headline inflation slowed in June but the core figure excluding volatile unprocessed food and energy rose
Euro zone businesses lost some momentum in June but chalked up their best performance last quarter in over six years.