There is no right time. If there is a third party involved, then that would not be a good time. Both spouses need to agree to attend with an open mind and a willing heart. But it is very common for one person to be going with a desire to reconcile, and the other to be just willing to attend, but not hoping to reconcile. The weekend works on teaching good communication skills. Whether you use those skills to rebuild the marriage, or cooperate on a divorce is up to the couple.
There are no religious requirements. It is open to everyone of any faith, or no faith. Retrouvaille does receive funding from the Catholic Church, which makes it much more affordable than private programs. The website is http://www.helpourmarriage.org. The contact person for your local group can give you more information. Feel free to call them.