Of course it costs them! Nationalisation just means the losses of the nuclear industry are born by the taxpayer, which will surface in worse services in other areas.
Fundamentally you can have high prices, shortages or you can disconnect France from the rest of the European grid but you cannot just have cheaper prices in France.
And nothing you've said seems to have relevance to shortages
As ClumsyPiloy said electricity is not something you can easily trade under the radar of the regulator. Technical limitations and regulation do change everything.