Getting rid of flea/eggs at home: Sprinkle a heavy layer of salt on your carpets and leave it down for a week. Then vacuum. It would be one of the safer things you could use for the cat - unless it has high blood pressure and a salt-jones.
Getting rid of fleas on pet: Once the cat and home are both flea-free, eucalyptus oil on the inside of the cat's collar will act as a natural repellent. My grandmother always kept bunches of cut eucalyptus in rooms (sometimes under the furniture) to keep the area flea-free and that has worked (those were the days before one could find the oil essence easily.)
I currently live in house with 3 giant eucalyptus trees on each side, so flea prevention isn't an issue for my 3 shaggy dogs. Not only is it natural, it smells good too!
Thanks for sharing Q!
[Image from Living Etc]