That's hard to say.
One day, the weather can be beautiful, the next day you see nothing because of fog and rain.
In spring it can already be warm, but it can also be cold and it can rain for days.
Sometimes in February all the snow on the Route Napoléon has melted. Sometimes the snow comes back in April. Even early in May, the route can be impassable because of the snow.
In the summer it can be hot, but also gray and wet.
So basically, you just need some luck for a nice crossing ...