I am doing LCHF and not paleo. So I have cheese and cream, very little fruit apart from tomatoes and such. As in paleo I stay off grains and this has made a world of difference to my bg as I couldn't cut out the sugar, soda, biscuits or other such stuff I've never eaten anyway.
It is important to take the HF part seriously, not only cut out the carbs. You need energy and fat is perfect. Not margarine though! Butter, lard, olive oil, coconut oil are fine as are nuts, cream, cheese.