The Ligue 1 outfit are 57 places ahead of their opponents in the French pyramid with Epinal battling against relegation to the amateur ranks.
Lyon, in contrast, are level on points with Paris St Germain and Marseille at the head of the top flight and Garde is determined to avoid an upset in the Vosges region of north-east France.
"It's always special for us to make our entry into this competition," Garde, whose side are returning from the winter break, said on the club website.
"We are playing against a team in Epinal who are not the best in their league. They have nothing to lose in front of their own fans.
"We have prepared well throughout the week in order to qualify and go as far as possible (in the competition). Why not keep the trophy?
"There are only a few teams who have done it in the past. It is a great challenge ahead."
The competition is no stranger to shocks with Quevilly, whom Lyon beat in last season's final, also in the third tier.
The 2009 winners were Guingamp and the second division side travel to Marseille on Sunday.
OM's summer signing Kassim Abdallah is fit after missing much of the first half of the season through injury and, having played in Ligue 2 last season for Sedan, knows how tough Guingamp will be.
"I know the team very well," the defender said. "They will be very motivated because they are playing against Marseille, for us the motivation is to not be the team that is knocked out by a Ligue 2 side.
"We want to go as far as possible in this competition so we will do everything to win."
The other side in the title race, PSG, travel to amateur side Arras, with the capital club's boss Carlo Ancelotti also targeting cup success.
The Italian said: "The Coupe de France is an important competition. We want to achieve something good."
Elsewhere on Sunday, there is a derby in Corsica as top-flight Bastia travel to third division CA Bastia. Montpellier go to Bourg-Peronnas, St Etienne visit Caen, Bordeaux head to Chateauroux, Lens host Rennes, Metz welcome Nice and Brest visit Lucon.
On Saturday, amateurs FC Drouais and FC Montceau Bourgogne take on Ligue 1 strugglers Nancy and Troyes respectively.
Sochaux, the other side in the Ligue 1 drop zone, head to lowly Thaon, while Evian travel to Amiens, Toulouse visit Boulogne and Lorient take on Chauray.
Ajaccio travel to Rouen, Reims visit Plabennec and Lille host Nimes.
On Monday, Valenciennes travel to Istres.