Paul uses the word Koinonia - the Koinonia of your faith will normally translate as the fellowship of your faith. Some versions do that. The communion of your faith is what he wants. J.B. Lightfoot translates it as
Richard D. Phillipsthe kindly deeds of charity that spring from your faith.Paul is praying that Philemon will embrace a lifestyle of generosity, as the overflow of his faith. Sharing in the faith means that Christians mutually participate in the gospel, in the power of God's grace. By the way, that is what the sacrament of the Lord’s supper is about. It is about a lot of things— primarily about the blood of Jesus and the assurance we have— but it also is that we are partaking together of one Christ; we are one in Christ. Paul wants him to have the Koinonia of his faith, the communion and fellowship of his faith. You see, if we mutually participate in the gospel, we must also participate in grace. Now here is the point that seems to have been lost on the Christians of Rwanda, and they are not the only ones, because countless other Christians seem to have not grasped this— that our faith in Christ must change the way that we relate to fellow believers.1
6 Je lui demande que ta participation à la foi soit efficace pour la cause de Christ, en faisant reconnaître en nous toute espèce de bien.