Normally unless its literally hopping alive with fleas I would simply suggest using “Shake n’ Vac” [UK powdered carpet freshener marketed by SC Johnson] or a fine powder such as baking soda. The way it is used is as follows, treat the cat with flea treatment. Remove pets and anyone who may have dust issues from the home and sprinkle the dust over the floor so that it has a fine but even coating making sure that you read the instructions and comply with the manufacturers guidelines.
Then take a torch or flashlight and zig-zag the beam across the floors covering all areas. The natural behaviour of fleas to a change in light and dark is to jump, in which case they will become coated in the powder and immobilised.
Leave the property alone for 1 hour then repeat the use of the flashlight and wait 15 minutes. Then simply clean the dust up with a vacuum cleaner and use a plug in flea trap for ongoing monitoring if needed.
Its an incredibly efficient way to physically remove fleas from an area as it relies purely on their physical removal rather than chemical action and as such you will never need to worry about resistance to chemicals and as a bonus your carpet and floors will be a lot cleaner.
We regret that we can offer no technical support on this application and respectfully ask that if you find this information useful please make a small donation to a registered Cancer charity as a way of saying thanks.