I'm not sure I get why everything above France would be rendered uninhabitable? The coldest place inhabited by humans year round is Oymyakon https://en.wikipedia.org/wiki/Oymyakon

Temperatures are generally above 0°C in summer, -50 approximately in winter.

Will an Ice Age actually be worse than that?

I would expect somewhat better, although maybe not much. I might expect Denmark and Southern Parts of Sweden and England to reach 10 degrees in Summer, and -20 in Winter. But that is of course just a guess on my part so I am certainly willing to hear that I have guessed wrong.