Some fans missed the start of England's win over Argentina in Marseille on Saturday and supporters trying to get to the stadium in Bordeaux to watch Ireland's heavy defeat of Romania suffered delays because of problems with the city's tram system.
"At the first match on Saturday between England and Argentina, we experienced problems with the influx of people who were unfamiliar with the Stade Velodrome," France 2023 president Jacques Rivoal said.
"This resulted in some of the fans entering the stadium after the match had started, which we of course regret and apologise for."
Tournament director Michel Poussau said he was "very confident" that any problems "will be fixed over the weekend" when Bordeaux hosts two matches.
Former England hooker Brian Moore described the scenes in Marseille before the Pool D opener as "beyond shambolic".
With the Olympic Games in Paris less than a year away, World Cup organisers are facing intense scrutiny.
In May last year, the Champions League final between Liverpool and Real Madrid at the Stade de France in Paris – which will host the Rugby World Cup final on October 28 – was delayed by nearly 40 minutes as fans struggled to get into the stadium after police funnelled them into overcrowded bottlenecks.
Police then fired tear gas at thousands of mainly Liverpool supporters who had tickets but were locked out of the stadium.
French officials initially blamed Liverpool fans, with Sports Minister Amelie Oudea-Castera blaming the English club for leaving its supporters "on the loose".
But an independent panel found European football's governing body Uefa and French authorities responsible for an incident which it said nearly caused "mass fatalities".
France's Senate, or upper house of parliament, concluded the problems were caused by a "string of dysfunctions", and Oudea-Castera said France had "learned lessons" from the episode.
