Both Benrahma and Fornals were hoping to leave the London Stadium after falling down the pecking order under West Ham manager David Moyes this season.
Lyon had agreed to sign Benrahma on an initial loan deal until the end of the season with an obligation to buy for around £15m in the summer, while Real Betis had agreed to sign Fornals for a fee in the region of £7m.
Benrahma had travelled to France to undergo his medical, but the deal collapsed at the 11th hour, much to the frustration of Lyon who have since released a strong statement slamming the "incomprehensible behaviour" of West Ham.
Lyon claim they had completed all the necessary documentation and procedures from their end to approve the transfer, but West Ham failed to submit the international transfer certificate before the deadline.
In response to Lyon's accusations, West Ham manager David Moyes responded to Lyon's accusations at a press conference on Friday, saying: "It's a big word to use before we get a chance to show exactly what happened or didn't happen."
Asked whether he feels that Benrahma would want to play for West Ham again, Moyes added: "I would expect so."
As for Fornals, the midfielder was in attendance at the London Stadium for West Ham's 1-1 draw with Bournemouth in the Premier League on Thursday night and was spotted pacing up and down the tunnel on his phone waiting to discover whether his move to Betis would go through.
However, Betis CEO Ramon Alarcon has since confirmed that a "computer problem" from West Ham's end has put the deal on the brink of collapse, although he remains "optimistic" that a positive resolution can be found in the "next few days".
On Fornals, Moyes said: "I think there is a chance the Pablo deal will be ratified. I can't confirm if it will or it not at the moment though."
According to the Daily Mail, both Lyon and Betis are now in contact with football's world governing body FIFA, who have launched an investigation into West Ham's actions for both deals involving Benrahma and Fornals.
A separate report from The Sun claims that both Lyon and Betis hope that FIFA will still allow the deals for the Hammers duo to go through.
Benrahma has spent the last three-and-a-half years with West Ham and has contributed with 24 goals and 19 assists in 155 appearances, including a memorable goal in the club's 2-1 win over Fiorentina in the Europa Conference League final last season.
However, the 28-year-old winger has been reduced to just five Premier League starts and a further seven across the Europa League and EFL Cup this season, failing to score and registering just two assists in the process.
Fornals, meanwhile, was signed for West Ham by current Betis boss Manuel Pellegrini in the summer of 2019 from Villarreal, and he has since played 203 times in all tournaments, scoring 23 goals and providing 19 assists.
The versatile midfielder has also struggled for regular game time this season, though, and has failed to score or register an assist in 11 starts and 12 substitute outings.