PARIS—When the sound of a suicide bomber detonating an explosive vest rang out across the Stade de France, President François Hollande was in the stadium watching France’s national soccer team take on Germany.

Within minutes, the French leader was given alarming news.

Paris was coming under attack from Islamic State militants, and Mr. Hollande had to decide whether it was safer to evacuate the stadium or keep thousands inside.

Huddling with at least two other VIP fans of Les Bleus—French Football Federation President Noël le Graët and France’s top cop, Interior Minister Bernard Cazeneuve—Mr. Hollande decided to let play go uninterrupted, according to French officials.

That meant French midfielders Lassana Diarra and Antoine Griezmann would continue maneuvering on the pitch while, on the other side of town, the players’ own family members became caught in the line of fire.