Frédéric Leclerc-Imhoff, 32, was covering an evacuation operation for broadcaster BFMTV when he died.
Officials say he suffered a fatal wound to the neck after shrapnel pierced the armoured vehicle he was travelling in. His colleague Maxime Brandstaetter was also injured, report say.
It was Mr Leclerc-Imhoff's second trip to Ukraine to cover the war.
He had been working for BFMTV for six years.
Paying tribute to him online, BFMTV wrote: "This tragic event reminds us of the dangers faced by all journalists who have been reporting this conflict at the risk of their lives for more than three months now."
BBC correspondent James Waterhouse says graphic images of what appears to be the aftermath have been circulated online, showing a badly-damaged lorry with a smashed windscreen and blood on the interior.
Another person travelling with Mr Leclerc-Imhoff, a local Ukrainian journalist, was not injured.
On Twitter, French President Emmanuel Macron paid tribute to Mr Leclerc-Imhoff and other journalists reporting on the frontline from warzones, saying: "I would like to reiterate France's unconditional support".
"Journalist Frédéric Leclerc-Imhoff was in Ukraine to show the reality of the war. On board a humanitarian bus, alongside civilians forced to flee to escape Russian bombs, he was fatally shot."
Meanwhile France's foreign ministry said it demands a "transparent investigation" as soon as possible to find out what happened.
In March, US journalist Brent Renaud became the first foreign journalist to be killed covering the war in Ukraine.