Christian funeral is a service for baptised Christians.
It is not a sacrament, but there is a very strong link between the baptism, which makes someone a Christian, and the funeral, where the public prayers of the church follows the sister or the brother who leaves for God.
Several symbols ( the sign of the cross, the wax candle, or the blessing of the deceased body with consecrated water) all along the funeral ceremony, remind us of baptism.
Therefore it is impossible for a non baptised person to have a Christian funeral celebration, unless the person was following catechism (young or adult on the way toward baptism), or if it happens to be a newborn child and the parents have not have the time -thou the intention - to have it christened.
It is true, in this trial, that during a moment spent in a church - and then, why not pray ?- is assuring for the persons close to the deceased. But sorrow should not make us forget respect for the last will of a person who never went to church during his life. And what sense can the symbols of the church have to a person who did not believe ?
This doesn’t prevent us from praying for the deceased or to have compassion for the family.