In this case, Uncle Sugar, being the French government, is on the hook.
I wondered about the question of insurance for Notre Dame Cathedral. Well, the answer is there is none!
In the vernacular, you would say they are "self-insured" with the French government responsible for the building. It is an answer for who is on the hook for rebuilding the church, it is the French people. In this case, they likely don't have an issue with that.
It is certainly not the same here in the United States with the separation of church and state being a bedrock (sort of) these days.
I'm a big believer in insurance, since most of us can't print money to make up for a deficit or loss. While $1B has been pledged by private interests to help with the rebuilding, the price tag might make that sum only about 10 percent or less of the total cost of rebuilding.
Whoever told the French president that the building could be rebuilt in five years was likely just returning from Amsterdam where he had been there smoking dope, as we used to say. I'm betting the full restoration will take 10-20 years.
One mantra I've always tried to follow is "Promise less, deliver more!"