They were arrested at the Mursitpinar border post close to the Syrian Kurdish town of Kobane on Thursday, Anatolia said, adding that they now faced deportation.
Paris-based freedom of expression watchdog Reporters Without Borders (RSF) confirmed the arrests.
Two of the Italians were correspondents for Italian state television station RAI while the French journalist was working for Le Figaro daily, Anatolia said.
Philippe Gelie, a senior editor for Le Figaro, told AFP that Samuel Forey had illegally crossed the Turkish border into war-torn Syria to cover the battle for control for the border town of Tal Abyad, that pitted the jihadist Islamic State group against Kurdish forces.
Kurdish forces took the strategic town earlier this week after several days of intense fighting, which sparked an exodus of more than 23,000 refugees into neighbouring Turkey.