Burnley defender Ward, 30, injured an ankle in the first half of Wednesday's dramatic 1-0 win over Italy.
The left-back missed training in Versailles on Friday morning.
On the plus side, Stoke striker Walters resumed training with the squad after missing the last two Euro 2016 games because of an Achilles injury.
On Thursday, manager Martin O'Neill said Ward's ankle had "blown up" after he picked up the knock in the first half of the game in Lille.
O'Neill is likely to be keen to retain Ward at left-back and allow Wednesday night's goal hero Robbie Brady to be used in the more offensive role he adopted to such good effect against the Italians.
The Republic players were back in training on Friday morning after being given the day off on Thursday.
O'Neill and his players did not get to bed until around 4.30 in the morning on Thursday after travelling back from Lille to their base in Versailles.
Inevitably, the pre-match discussion about Sunday's game in Lyon includes mention of the Republic having the chance to avenge the incident in November 2009, when the Irish missed out on qualification for the World Cup finals in South Africa thanks to a decisive goal that saw Thierry Henry handle the ball in the build-up.
However, O'Neill says the current Republic squad have "decided to forget about it".
"It will be a talking point obviously but I don't think it will concern us when we play the game," added O'Neill.
Republic of Ireland full-back Stephen Ward is a fitness doubt for Sunday's Euro 2016 game against France but Jonathan Walters may return to action.