Rather than Brest of course now Monaco is closer to playing in the Champions League next season as you said, while Brest at this time of course they have been on edge after Lille also put pressure on Brest again with a difference of 1 point at this time, indeed Brest still has a chance to qualify for the Champions League next season even though they will drop to rank 4 later, But being in 4th place of course they have to do a playoff match to get a ticket to the Champions League so I think it will be quite difficult.
I think Brest still have a fair chance here because Monaco and Lille will face each other that certainly will give advantage to Brest. If Monaco win against Lille, Brest will stay third, but if Lille win, Brest will be fourth with two points gap. This situation will still give hope for all three teams. It depends on who have the strongest consistency till the end of the season.
It's still quite difficult to predict who will stay in Champions League zone, because anything can still happen. Looking at the remaining opponents for the three teams, I think Brest have the bigger hope, because they will play against teams that dont have any thing to fight for any more, While Monaco and Lille will play against teams those are fighting for staying in Ligue 1.
It is pretty much the game of the season for both Monaco and Lille. If Monaco wins it, the Champions League qualification is essentially safe. I know that mathematically something could still happen, but it would be 80% of the way I think. For Lille it would be important to keep the distance to Nice, depending on how they play, but a win would obviously be a very nice outcome. Because there is still a game to be played against Nice and having some advantage in hand would make that final game of the season an easier one.
But it is such a close race for the time being. What a success it would be for Brest to get a Champions League spot. I don't know wheter they ever played in that competition, but it is possible now. The discontinuation of their strong streak comes at a very bad moment now, but if they could score a 4/4 in the last 4 games, I guess it would be enough.