The two "intercept" jets first fly to within a kilometre (half a mile) behind the "bogey", as an unidentified plane is called.
Four French Mirage jets this week completed a four-month tour of duty in Lithuania -- and their crews were busy, engaging with Russian planes on 23 occasions.
"We use the term 'intercept' but it is better to say 'identify' and 'observe'," Lieutenant Colonel Isaac Diakite told AFP at the base in the freezing surroundings of Siauliai in northern Lithuania.
"The Russians take care to remain in international airspace, flying along the Baltic area without going into it. They have a right to be there, but so do we," he said.
"So we take off to have a look, identify the plane and photograph it, to show we're there."
Russian planes have been flying close to NATO's northern border for several years now, and the number of flights increased after the Ukrainian crisis started in 2014.
"It's a little game, a demonstration of strength to show that they are back after their fleet underwent large-scale modernisation," said General Olivier Taprest, commander of France's aerial defence, who took part in a ceremony in Siauliai to mark the end of the deployment.
NATO radars regularly pick up Russian Sukhoi fighter-bombers, Antonov transport planes and strategic long-range Tupolev bombers crossing the so-called Omega Line, NATO's self-imposed line that runs from the north of Norway. Crossing it triggers alerts at NATO bases and planes are scrambled.
Tupolev bombers were spotted three times in the final months of 2016, flying over the Baltic states and to the west of the British Isles.
A year earlier, in November 2015, Tupolevs were even recorded flying around Ireland and across the Mediterranean to drop bombs in Syria before heading back to Russia through Iranian airspace.
It was done, the French officers said, merely as a show of force to the Americans.
"It was completely useless from a tactical point of view, but it sent a message: if you calculate the distance flown, it shows you could reach New York," General Taprest said.
NATO's jets are rather like guard dogs kept behind a fence, without ever actually biting or even barking -- their presence is to show Moscow that the transatlantic alliance will defend its members' skies and approaching the limits of that will provoke a reaction.
The procedure is strictly ordered.
The two "intercept" jets first fly to within a kilometre (half a mile) behind the "bogey", as an unidentified plane is called. Then one of them moves next to the wing of the target at a distance of between 300 metres (yards) and 50 metres.
The aim, clearly, is to let the pilot know he is being watched.
"If it's night-time, we shine a light into their cockpit," one of the French pilots, who wanted to be identified only by his nickname "Rom's", told AFP.
"Sometimes they respond with their decoy flare, sometimes they don't. Then we switch to autopilot to allow us to take photographs which are then sent to the military command."
If the Russian plane does not deviate from its course and remains in international airspace, no further action is taken.
However, if the plane intrudes into NATO airspace, the response ratchets up in several steps, starting with the firing of a decoy flare until actual warning shots are fired. The final response would be launching a missile to down the plane.
"We can try to contact the Russian pilot over the radio on the aeronautical emergency frequency. Sometimes they reply," Rom's said.
When pilots fly side-by-side at a distance of 50 metres, they can see each other up close and can even signal to one another.
"But most of the time they don't look at us. They have their path to follow and they don't deviate from it," he added.