First of all don't use gravel as backfill, since it is not a filter and can plug. ASTM C-33 Concrete fine aggregate is best (Concrete sand).
In some areas it is a good idea to do some interior drainage also, since water under pressure from a distance can rise up due to that pressure inside the basement (I've seen that). There we solved it by underlaying the slab with clean sand and placing the pipes at no more than 15 foot spacing, since the hydraulic gradient in sand was 7:1 flowing laterally. Yes, then the interior pipes at the footing also are needed (in addition to those outside).
In addition, remember that surface water on the ground outside can seep in much more easily in that loose backfill than beyond, so divert all surface water away with positive slope. Many more basement problems are due to surface water getting down there, rather than ordinary high ground water at basement level. Extend downspouts out beyond the backfill. That may mean at least 10 feet out. I speak from experience in the house I recently moved into. Former owner had a sump pump running frequently with every rainfall. After I fixed the outside, sump pump never runs. My fix consisted of waterproofing the ground surface also with a mix of bentonite at 5 percent in 4 inches. 10 ft. extensions on the downspouts also.