> Mandatory warranty
> the manufacturer has to prove
Just nitpicking: the mandatory warranty ("Gewährleistung") is supplied by the seller, not the manufacturer. As a consumer you don't need to deal with the latter no matter what the former is trying to tell you. In the same line, the burden of proof after six month is on the seller not the manufacturer.
A manufacturer often has an additional voluntary warranty ("Garantie") distinct from that.
That is the case (including the role of the seller) across the whole EU by Directive 1999/44/EC (although member states can go beyond that and often do by e.g. extending the time).