I think it is the State Legislature that must overturn the moratorium. I've not heard many calls for it. The Gov. who imposed it did so because a slew of people on Death Row were proven innocent or did not get fair hearings. So he said, no death penalthy until we can insure no innocent people are put to death. Which is an impossible standard and in effect abolishing the dealth penalty without having public support to do so.
I suppose it could be brought back, depending on the circumstances. But I think there is a lot of death/outrage fatigue in the country at the moment. "Pretending that you already know the answer when you don't is not actually very helpful." ~Migeru.
The other possible reasonis that it may say in the French constityution that citizens cannot be extradfited to third party states under certain conditions. As An example of something like this look at Ronnie Biggs one of the UK's great train robbers. He fled to Brazil, and managed to avoid extradition for 16 years as he had fathered a Brazilian child, and under Brazilian law, he had to remain in Brazil to pay for the childs upkeep. Any idiot can face a crisis - it's day to day living that wears you out.