The two-year government bond yield was on track to finish the month down about 11 basis points, the biggest drop since February 2013.
French 10-year bond yields were set for their biggest monthly fall since June 2016, down 19 basis points.
As worries over France and the potential break-up of the euro zone have receded in the past week, so has demand for German government bonds - regarded as among the safest assets in the world.
In contrast to France, German 10-year bond yields were set to end April marginally higher and the week 8 bps higher - the biggest weekly rise since early March.