Jose Mourinho's side will host the French club in the first leg on February 16 at Old Trafford, with the return the following week.
"That's a nice thing. Paul was already laughing about it and for sure his brother is also laughing," Mourinho said, after Monday's draw in Nyon made it a Pogba family affair.
"It has happened a few times in the history of football and it's a nice thing."
United midfielder Paul represents France but Florentin, a defender, plays for Guinea and the brothers have never faced each other in a competitive game.
At age 26 Florentin Pogba is three years older than his more famous sibling, who cost United 89 million pounds ($109 million, 100 million euros) from Juventus in the summer.
The other Premier League representative, Tottenham Hotspur, will face Gent of Belgium after being eliminated from the Champions League at the group stage.
Villarreal of Spain will face Italian giants Roma in one of the standout ties, while Bundesliga club Borussia Moenchengladbach were drawn against Fiorentina of Italy.
United and Saint-Etienne met in the now-defunct Cup Winners' Cup first round in 1977, with United winning 3-1 on aggregate.
On that occasion United were forced to host the second leg in the southern English city of Plymouth, 450 kilometres away from Old Trafford, following crowd trouble in the first leg in France.
Mourinho's men finished second in Group A behind Fenerbahce of Turkey while Saint-Etienne topped Group C.
After also having to go to Ukraine to face Zorya Luhansk in the group stage, United's Portuguese manager is pleased that there will be no long away trip this time.
"The good thing is the travel distance. We were very unlucky in the group phase, we had to go very far, it was very difficult to go to Turkey, Ukraine," he said.
"Now we go to France because the flight is easy and it's not an easy period, there are lots of games, so that is good."
Saint-Etienne, 10-time French champions and European Cup runners-up in 1976, are eighth in Ligue 1.
"Saint-Etienne is a historic old club with lots of tradition. People of my generation will never forget that (Michel) Platini team and it will be difficult because every team now is a good team in the competition," added Mourinho.
"For sure, Manchester United is one of the big names in the competition but we have two months without the Europa League, two months to forget it, then we will see."
Saint-Etienne will host United in the second leg at the Stade Geoffroy-Guichard on February 22, with that game brought forward a day to avoid a clash with Lyon, who play AZ Alkmaar of the Netherlands nearby the following day.