Giorgi's modified Skoda Fabia R5 did not comply with the governing body's technical regulations and was only seen by the FIA on the day of scrutineering for the Bastia-based event, where it was questioned by officials.
The FIA's concerns centred on the legality of a wheel-mounted throttle and brake system produced in Italy that the 33-year-old driver from Corsica, who was paralysed in a motorbike crash 10 years ago, had planned to compete with.
Giorgi said: "When going to scrutineering, the commissioners of the international federation [FIA] found several excuses not to validate my registration."
Initially there was a problem with the fire extinguisher mountings. Giorgi added: "They ask us to hang them with metal not plastic.
"We did that. But when we came back to see them, they tell me: 'Anyway with the system installed on your vehicle, it will not pass'."
Co-driver Jean-Paul Marchini said Giorgi had spent €35,000 on what would have been his first Tour of Corsica entry.
Marchini added: "The FIA refused to allow us to compete. I am disgusted."
A statement from the FIA issued during the event read: "Car #50 was presented at pre-event scrutineering with numerous modifications which had not been communicated to the FIA in advance, per procedure.
"No certification of adaptations for vehicles of disabled drivers had been requested by the competitor, pursuant to Article 10.3 of Appendix L of the 2019 International Sporting Code.
"In an effort to support the entrant's participation, the FIA immediately convened its safety, legal, technical and sporting departments.
"Preliminary information was given to the stewards by the FIA technical delegate and an official report prepared in relation to the modifications required to accommodate the competitor's needs and comply with the regulations.
"Despite their concerted efforts, due to the very short timeframe it was not possible to complete the certification process and ensure safety standards were not compromised before the deadline.
"The FIA was left with no alternative but to inform the competitor that he was not allowed to start the event."
FIA rally director Yves Matton told Autosport his team had done all it could to help Giorgi.
"Everybody got involved with this," said Matton.
"All our departments worked to make it happen, but it was just too late.
"If we had seen the car and been made aware of these changes on Monday or maybe even Tuesday it might have been possible, but by Wednesday it was too late."