The Athena-Fidus satellite, operated jointly with Italy, was approached "a bit too closely" by Russia's Luch-Olymp craft, known for its advanced listening capabilities, Parly said.
"It got so close that we might have imagined it was trying to intercept our communications," she said at France's National Centre for Space Studies (CNES) in Toulouse, southern France.
"Trying to listen to your neighbours is not only unfriendly. It's an act of espionage."
Parly said officials took the "appropriate measures" and continued to monitor the satellite after it left, and observed it manoeuvring near other targets as well, she said.
Last month Washington accused Moscow of developing anti-satellite weapons and cited "very abnormal behaviour" of a "space object" deployed by Russia last October.
It also dismissed a proposed treaty by Russia and China aimed at averting a space arms race, calling it "hollow and hypocritical".
"We are well aware that other major players in space are deploying intriguing objects into orbit, experimenting with potential offensive capabilities, conducting manoeuvres which leave no doubt as to their aggressive intent," Parly said.
French President Emmanuel Macron has pledged to develop a "space defence strategy" for France, and Parly said experts were preparing recommendations she intended to pass on by the end of the year.
"We're at risk, our communications, our military manoeuvres and our daily operations are at risk if we don't react," Parly said.
She noted the call by President Donald Trump last month to create a new "Space Force" to assert US dominance in orbit and protect against vulnerabilities to its satellite-based systems.
"I've heard some people laugh" about Trump's plan, Parly said, but "I'm not among them".
"I see this as an extremely powerful signal, one of confrontations to come, of the increasing importance of space, of the future challenges," she said.
"We know that space is becoming militarised. We're not going to stand by and watch."