I would first see if the first part of Andre's answer is feasible. If not, the second part of Andre's answer will work but that method will result in all parts of all polygons being made into single-parts which may not be desirable (UK or Greece for example have many islands which you may not want to subdivide).
An alternative is to use the
Split selected multi-part features to single part tool in the
Advanced Digitizing tools plugin. To do this, select Germany (currently including Corsica) and then click on the little drop-down arrow on the first split tool. This will give you a little menu of two items and the tool you want is the second one (which is why you don't normally see it by default). Click that tool. The split is done but you don't get any message and both parts will still be selected, so confirm that Corsica is now separate by deselecting everything and then selecting just Corsica. You will then need to correct the attributes for Corsica (as they will still be 'German') and if you have any attributes showing land area - those may need recalculating too.
Make sure you are using the ADVANCED digitizing tools plugin as below and not the ordinary one.