These are species with at least one recorded territory in French Guiana, not a national checklist: a bird list from eBird or Avibase is more complete. The counts follow recording effort as much as wildlife, so a country with more visitors and more naturalists will show more of both.
The species with the most open occurrence records in French Guiana, among those a photograph exists for. Most recorded is not most numerous: it rewards animals that are common, conspicuous and live where people go.

Pecari tajacu

Ramphastos tucanus

Ramphastos vitellinus

Tayassu pecari

Sapajus apella

Ramphocelus carbo

Ateles paniscus

Psophia crepitans

Progne chalybea

Saguinus midas

Saimiri sciureus

Tapirus terrestris
The reference database has no regions filed under French Guiana.
The field guide covers French Guiana on the map, but none of its species have an entry written for them yet.