Les Aiglons fell to a 2-0 defeat to league leaders Lille last time out, while Brest were thumped 4-1 by relegation candidates Nantes.
Nice's European prospects were already hanging by the thinnest of threads before they travelled to table-topping Lille, and a 13th-minute strike from Burak Yilmaz set Les Dogues on their way to a comfortable triumph over Adrien Ursea's inconsistent crop.
After being reduced to 10 men following the sending off of Jordan Lotomba, Nice were never expected to spring a surprise in the second 45, and a stunning volley from Zeki Celik saw Lille ease to a 2-0 victory and kill off any faint hopes of a top-five charge for Les Aiglons.
Ursea's side have produced the goods more often that not in the past couple of months, but it has been a case of too little too late for Nice, who lie smack-bang in the middle of the table in 10th place and realistically cannot challenge for a top-seven spot anymore.
Defeat at Lille represented just their second loss in nine league outings - a run which also includes five victories and two draws - but with star man Amine Gouiri picking up an injury at the worst moment possible, any prospects of a strong end to the season are shrouded in uncertainty.
However, Les Aiglons are welcoming Brest to a ground where they have taken 10 points from the last 12 on offer - conceding just twice in that time - and their upcoming opponents still have a bit more work to do if they are to guarantee survival.
Brest's commitment to attacking has seen Olivier Dall'Oglio's men play out some thrilling encounters throughout the campaign, but the out-of-form Pirates were on the wrong end of a goal-laden performance from Nantes in gameweek 35.
Les Canaris are fighting for their lives at the foot of the table and lost defender Jean-Charles Castelletto to an 11th-minute injury, but Brest produced a totally lacklustre performance and succumbed to goals from Moses Simon, Ludovic Blas, Imran Louza and Kalifa Coulibaly before Romain Faivre's late consolation.
Having claimed just one win from their last seven in Ligue 1, Les Pirates have slipped to 14th in the table and are not mathematically safe from the threat of relegation just yet, but they remain six points clear of Nantes in 18th spot despite being humbled by Antoine Kombouare's men on Sunday.
Brest's 48 goals at the correct end of the pitch is by far the highest tally in the bottom half of the table, but 61 shipped at the other end is the fourth-most in the league and pinpoints where their problems lie, especially seeing as they travel to Nice boasting just one clean sheet in their last 11 away matches.
Two quickfire goals from Steve Mounie and Franck Honorat helped Brest secure a 2-0 win over Nice earlier in the season, but Les Aiglons have not suffered two defeats to their visitors in a league campaign since 1989, which was the last time that Brest picked up all three points on Nice's turf.
Nice can look forward to the long-awaited return of star man Gouiri this week after he resumed team training, while his fellow protege Khephren Thuram could also be available after being pictured in the same session.
Changes should be afoot after an embarrassing day at the office against Nantes, potentially starting with Jean Lucas returning to the engine room after he set up Faivre for their late consolation on that day.
Steve Mounie was introduced at half time against Nantes and could lead the line alongside Gaetan Charbonnier, who has scored four of Brest's last six league goals on the road.
Nice possible starting lineup:
Benitez; Atal, Saliba, Todibo, Kamara; Schneiderlin; Lopes, Boudaoui, Claude-Maurice; Gouiri; Dolberg
Brest possible starting lineup:
Larsonneur; Pierre-Gabriel, Chardonnet, Brassier, Perraud; Honorat, Belkebla, Lucas, Faivre; Mounie, Charbonnier
We say: Nice 2-0 Brest
Brest's leaky defence has hampered their aspirations of a top-half finish all season long, and they could be in for another rough ride against a fit-again Gouiri.
Nice are only playing for pride as well, but Ursea will not want them to take their foot of the gas at this late stage, so we can envisage a routine win for Les Aiglons this weekend.