Southgate is aiming to take England to the semi-finals for the second World Cup in succession, but standing in their way are the reigning champions.
While Deschamps has been lauded for taking France to the title in Russia four years ago, Southgate came under scrutiny in the lead-up to the finals in Qatar after a winless run of six games saw England suffer Nations League relegation.
The former defender has been in charge of the national team since 2016, with the semi-final spot at the World Cup followed by a penalty shootout defeat to Italy in the Euro 2020 final last summer.
"I very much like Gareth," Deschamps said on the eve of the game at Al Bayt Stadium.
"We have met on a number of occasions and have talked about a number of things.
"Not everyone appreciates him so much in his own country, that isn't because he wasn't a good footballer himself - he had a long and distinguished career and he is also a very good coach.
"He has enabled England to get some very good results over the years and I very much like him."
Most of the talk in the build-up to the fixture has surrounded Kylian Mbappe, the Paris St Germain forward who has already scored five goals in Qatar to lead the race for the Golden Boot.
England's players have been keen to stress that France have other players who need to be kept quiet, but Deschamps conceded Mbappe could be the man who makes the difference after scoring a brace in their 3-1 win over Poland in the last round.
"I'm sure England will have prepared to face Kylian, as our previous opponents did," added the one-time Chelsea midfielder.
"But he is in a position to make the difference. Even in the last match when he didn't have his best match, he didn't show his top form compared to previous games, he was still decisive.
"We have other players that can be dangerous as well and that helps us not to be over-dependent on Kylian. But Kylian is Kylian, and he always will be.
"He has that capacity to make the difference at any moment in the match."