Spider might help...but it's probably not fruit flies. If it's localized around your seedlings it's probably fungus gnats (which I recently learned are totally different from fruit flies). Let your soil dry out good before the next watering and it'll take care of the fungus gnats. After that the spider's fate is in your hands. I'd say place him outside in the garden. Spiders are a welcome visitor in my garden!!!!
USDA Zone 7a, Sunset Zone 32.
Failure is only a fact when you give up.