Frontline and Advantage WILL work, but it will take a few months. Truly, ANY method of flea control will take months to work.
You have to understand the flea life cycle to understand why. 95% of ALL The flea population in your home are EGGS. Every day that you have fleas, those adult fleas are adding to those eggs. You must continually kill all the adult fleas EVERY DAY in order to stop the reproduction, and THEN you have to let the eggs hatch into pupa (because you won't get ALL of the eggs not even with sprays and vaccuming), and then the pupa into baby immature fleas (these can't reproduce). Now, if you have a topical flea product on at this time, the immature fleas will bite the animal and will die before they can reproduce more eggs. If you aren't killing these fleas daily, the cycle will go on and on and on and on.
I recommended Advantix or Advantage. The vet I work for is having us stray away form Frontline, because soon it will be available in all retail stores, instead of just vet offices. Stay away from Bio Spot and all the other crummy products you find on the shelves of normal stores. They contain just a wee bit of the chemical that kills fleas, and the fleas can actually build up a resistance.
You'll need to do a LOT of vaccuming, a lot of laundry, a lot of bathing/flea dips (every day) if you want to get rid of fleas without chemicals. Growing up we had fleas with the dogs and we didn't use chemicals. The BEST we could ever do was to keep fleas to a minimum, but we NEVER got rid of them entirely until all the animals were on a topical flea preventative.