The six were detained soon after the attack two weeks ago in a remote, forested area in Datia district in central Madhya Pradesh state where the woman was camping with her husband.
The trial opened with two prosecution witnesses recording statements and identifying possessions stolen from the Swiss couple that were recovered by police, the Press Trust of India reported.
The Swiss couple were not present during the proceedings and the court is likely to ask them to appear before it, the news agency said.
Judge Jitendra Kumar Sharma said the next hearing will be held in April when another prosecution witness, who helped the victim, will testify.
The Swiss woman was allegedly gang-raped on March 15. Her 30-year-old husband was tied up as the woman was assaulted and the pair were also robbed, according to police.
Only four of the six were charged with gang-rape because testimony from the victim said two of them were "only present at the crime scene", according to M.L. Dhody, a Datia police officer.
The other two accused are charged with assault and robbery.
Five of the suspects are farmers in their twenties while the sixth is 19, police said.
The incident came three months after the fatal gang-rape of a 23-year-old physiotherapy student on a bus in Delhi, which sparked nationwide outrage.
The public anger prompted parliament to toughen sex offence laws including doubling the minimum prison sentence for gang-rape to 20 years.
The Swiss couple were cycling through northern India. The accused allegedly saw the pair pitching their tent and attacked them.