Coudet played for the Union in their friendly matches against Celtic and Manchester United.
The team will play a friendly against the host Harrisburg City Islanders on Tuesday night.
In their next MLS game, the Union (4-8-2) will host the New England Revolution (4-9-2) Saturday at 3:30 p.m. at PPL Park.
Union team manager Peter Nowak said he believes Coudet will be in the lineup against New England.
He plans to take a wait-and-see approach with Mapp.
Mapp "is a very intelligent guy and has been in the game many years, and over the course of time he will need to adjust to our players and training methods," Nowak said.
"We will find out more about him as soon as we start working with him."
Coudet is expected to make an immediate impact.
"I think he brings a calmness to the team and a good flow to the game," Nowak said.
Nowak indicated that another move could be in the offing.
"We think competition is good within the team and I believe those two signings and another that could be coming up gives us the opportunity to mix it up," he said.
"We need to stay fresh and have competition within."
Contact staff writer Marc Narducci at 856-779-3225 or mnarducci@Phillynews.com.