Gasquet told the Court of Arbitration for Sport on Tuesday that he failed a drug test in March because he kissed a woman in a nightclub who contaminated him with cocaine.
He was suspended for 2 1/2 months but the World Anti-Doping Agency and International Tennis Federation appealed to CAS to give him a doping ban of at least one year.
CAS secretary-general Matthieu Reeb said a verdict is expected in early December.
"Everything went as expected and Richard Gasquet has, of course, had his chance to speak," Reeb said after the seven-hour hearing.
"Now the arbitrators will begin their deliberations, which are going to take around three to four weeks until a final judgment will be communicated to the parties."
That would allow Gasquet, who was suspended for the French Open and Wimbledon, to prepare for the Australian Open in January if he is cleared by the CAS panel of three lawyers.
"That is part of their considerations," Reeb told The Associated Press.
Gasquet declined to speak as he left court. While lawyers for the ITF described the process as "very good and very fair."
The 23-year-old Gasquet tested positive the day after pulling out of the Miami Masters with a shoulder injury. Cocaine is classed as a stimulant if an athlete uses it during competition.
In evidence to an independent tribunal called by the ITF in July, Gasquet said he visited a music club in Miami that night and met a woman identified only as "Pamela," who he kissed several times.
The tribunal panel accepted that he was "contaminated with cocaine" by the woman and not to blame for the positive test, describing Gasquet as "shy and reserved, honest and truthful" and clearing him to resume playing immediately.
WADA and the ITF believed he should be held to the strictest standards of the WADA Code _ which makes athletes responsible for any substance found in their body _ and denied the defense of "no significant fault or negligence."
Gasquet's ranking peaked at No. 7 after he reached the Wimbledon semifinals in 2007. It dropped from No. 23 when his failed test was announced in April to currently stand at No. 53.