The project was approved by the city's government two years ago but the tribunal ruled that the local residents' complaints were not thoroughly considered and the fee payable by the French tennis federation was set too low.
The extension, which the FFT said would cost 273 million euros, has been fought by residents' associations because the building work would encroach on the nearby Auteuil botanical greenhouse complex.
The FFT said it would appeal.
"The French Tennis Federation has noted with astonishment the decision of the Administrative Tribunal of Paris," a statement said.
"Contesting the grounds for the annulment and convinced the project is respectful to the site, it will appeal the decision and request a stay of execution."
The mayor's office was equally shocked.
"The City of Paris is determined to achieve this beautiful project for Paris and will promptly agree with the FFT on the way forward."
The venue for the French Open, the second grand slam tournament of the season which welcomes over 400,000 spectators in late May and early June, has been in need of renovation for years.
The FFT has said that after an extension, the French Open would be equipped with a centre court with a retractable roof.
The federation also guaranteed "increased levels of comfort and more room for all involved (players and spectators) and a stadium with the latest in terms of infrastructure".
- Politics & Government
- French tennis federation