Carla attended the memorial service at the city's Saint-Sulpice church with her husband, Chirac's successor Nicolas Sarkozy, while Salma arrived with her spouse, French billionaire Francois-Henri Pinault.
The service was part of a national day of mourning, and took place after a military tribute at the Les Invalides complex, which houses Napoleon Bonaparte's tomb, presided over by France's current president Emmanuel Macron.
World leaders past and present including Vladimir Putin, and Bill Clinton were also present, while Prince Edward represented the British royal family.
Chirac, who served as President from 1995 to 2007, died last Thursday at the age of 86, after a long battle with ill health.
France's presidents have in the past been mourned with a service at Paris' famous Notre Dame cathedral, but the landmark was ravaged by fire earlier this year.
Following the fire, Salma's husband, the head of French luxury group Kering, and his father Francois pledged around $110 million (£89 million) to help with the cathedral's restoration.