French Open organisers estimate up to 60% of the usual capacity will be allowed inside Roland Garros when the rescheduled event is held in September.
A maximum of four people will be able to sit together on the main courts with an empty seat between groups.
On the other courts, one seat out of two will be empty when the main tournament starts on 27 September.
The US Open is being held without any spectators in attendance in New York from 31 August to 13 September.
Wimbledon was cancelled this year for the first time since World War Two because of the coronavirus pandemic.
The French Open was postponed from its usual May-June dates and French federation president Bernard Giudicelli said about 20,000 spectators are expected during the early stages of the two-week Grand Slam, with around 10,000 on the day of the final.
Those numbers could still change if the French government revises its current social distancing rules.
Of the show courts at Roland Garros, Court Philippe-Chatrier's usual capacity is 15,500, so a 60% capacity would allow more than 9,000 fans in.
Court Suzanne-Lenglen usually holds 10,068, while Court Simonne-Mathieu seats up to 5,000.
A record 520,000 fans attended last year's event.
"We went for the responsible option," said Giudicelli, who added that wearing a protective mask would be mandatory for people moving around inside the grounds, while it would only be recommended for people sitting courtside.
"Should the situation evolve in the right direction, new tickets would be available in September," he added.