"We are conscious that this kind of phenomenon (racism) does not disappear overnight," Gaillard told a news conference.
"We have clearly emphasised that we will back drastic measures to deal with drastic behaviour. Stopping games is a drastic measure and carries a point penalty for the home team as it is considered a 3-0 loss," Gaillard added.
Gaillard, attending a "Unite against racism" conference in Warsaw, said UEFA had already shut down stadiums and banned teams from tournaments due to fans' bad behaviour.
Earlier this week former England defender Sol Campbell called on the English Premier League to dock points from clubs whose fans were found guilty of indecent and racist chanting.
Portsmouth captain Campbell has been the target of verbal abuse from Tottenham Hotpsur fans since leaving to join arch-rivals Arsenal in 2001.
In January 11 supporters were charged with indecent chanting towards him during a league match between Portsmouth and Spurs last year.
Poland, set to co-host the European Championship in 2012, suffered a string of anti-Semitic and racist incidents late last year which triggered a debate about racism among Polish soccer hooligans.
Gaillard said racism issues would not hamper Poland's preparations for the tournament as they were not one of the requirements taken into account.
Spanish football has also had problems with racism.
Former national coach Luis Aragones hit the headlines in 2004 for derogatory comments about French player Thierry Henry although he has always denied they were racist.
Large-scale racist abuse was directed at visiting black players during a subsequent friendly international against England.
In 2006 Barcelona striker Samuel Eto'o thereatened to walk off the pitch after being racially insulted by fans during a match against Real Zaragoza.
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