The European Championship runners-up overcame heightened expectations and a nervy start in Al Khor to triumph with ease against the Africa Cup of Nations winners on Sunday evening.
Harry Kane opened his account in Qatar - becoming England's highest ever scorer at major tournaments and moving within one goal of Wayne Rooney's record - after Jordan Henderson opened the scoring late in the first half.
A smart Bukayo Saka clipped effort wrapped up a comfortable 3-0 last-16 win against Senegal that secured a return to Al Bayt Stadium on Saturday to take on World Cup holders France.
"It's the biggest test that we can face," England boss Southgate said.
"They're world champions, incredible depth of talent, outstanding individual players, very difficult to play against and to score goals against.
"It's a fantastic challenge, brilliant game for us to prepare for.
"The two quarter-finals that are already in place are fantastic, historic football rivalries and great games from the past.
"A brilliant game for us to be involved with and test ourselves against the very best."
France eased past Poland earlier in the day to seal their spot, with Olivier Giroud becoming their all-time top scorer before Kylian Mbappe hit a brilliant brace in the 3-1 triumph.
"Of course (Mbappe) is a world-class player and has already delivered big moments in this tournament and in previous tournaments," Southgate said.
"But there's also, I think (Antoine) Griezmann is now over 70 consecutive games for France and I think he's also a phenomenal player.
"We know Olivier Giroud so well and they have outstanding young midfield players as well.
"So, everywhere you look when we're studying France at every age group, they have incredible depth of talent in every position.
"It's a huge test but one that we're really looking forward to and it's a great challenge for our team now."
It remains to be seen whether Raheem Sterling will be involved against France, having been allowed to leave the camp ahead of the Senegal match.
The PA news agency understands armed intruders broke into the 27-year-old's house while his family were there on Saturday evening, leaving him understandably shaken and concerned about the well-being of his children.
Sterling has headed back to the UK but could return if the circumstances are right, with Southgate saying "we've got to wait and see" if he features again in Qatar.
"Raheem, as the FA statement says, is having to deal with a family situation, so he's going back to England," the manager said.
"We've got to give him time to try to resolve that or be there for his family. That's the most important thing at this time, so we're going to give him that space.
"It didn't impact team selection. I spent a lot of time with Raheem this morning, but you know you have days where events happen and you have to deal with them.
"He's on his way home and, yeah, we're obviously mindful of him being allowed space and (having) privacy respected, so we don't want to talk in too much detail.
"Of course it's not ideal for the group ahead of a big game but it pales into insignificance - the individual is more important than the group in those moments.
"So, I needed to look after the situation and then I had to pass it on to others to deal with this afternoon in order to get him home."