How does a person determine whether they are a "false Christian" or "inconsistent Christian"?

First, there is a framework in the Bible to help believers identify themselves as being ‘genuine’ or not. However, although this framework is infallible to guide the elect into an 'assurance of salvation' it provides no reliable means to an unbeliever. A wicked soul can and will deceive themselves as part of the curse they are under. Secondly, this framework is ‘personal’ as it involves the ‘internal witness’ of the Holy Spirit and does not extend to an infallible judgment of another person's state. There is a framework for that (for discerning the sate of others) but it is more general and less determinative primarily for the purpose of identifying false teachers. To answer your question then I will define the scope to be; “an individual who is trying to determine for their own conscience sake, whether they are really saved or no.” I am answering as someone who firmly believes in once saved always saved. Naturally the question therefore as regarding whether my faith is genuine or not is the most important question I could ever ask myself.

In a nutshell: Anyone who has genuine faith in Christ by relying on his death, in order to be relieved from a genuine sense of condemnation and fear of eternal punishment for their sins and a corresponding genuine relief of that fear by faith, is most likely a genuine believer. The question therefore amounts to how can one determine ‘a genuine fear of hell’ and a corresponding ‘genuine relief and peace with God’ by trusting in his death for one’s forgiveness and justification. To answer one first must be clear that such faith is truly in Christ and not based on works of the law, or practicing any religious rules under any Church claimed authority, effectively replacing faith in Christ with faith in Church, church doctrine, or church practice. In essence if one has never even accepted that a person can be saved by doing nothing more then simple faith, then they are automatically excluded from having any biblical assurance of salvation as they are trusting something in addition to a personal reliance on Christ's work. In addition anyone who has this genuine conviction that Christ’s death is sufficient to provide salvation apart from works of the law, baptism into a particular denomination, or any other external work, has only genuinely come to share in that faith if they are found to persevere to the end with it:

We have come to share in Christ, if indeed we hold our original conviction firmly to the very end (NIV Heb 3:14).

Therefore one part of the framework is that ‘faith in Christ’ as a means to obtain peace from a fear of eternal damnation can’t be fully destroyed in one who has come to have it. Although this is only a guide it is very helpful because a person who thinks they had become a Christian but then falls into various sins and begins to deny that they had salvation and no longer has any relief of salvation and no longer feels any need for relief because they no longer fear eternal damnation for the guilt of their sin, which faith is to relive, has obviously never been saved in the first place.

We have now narrowed the question therefore to those who have fallen into various external, or internals sins, yet still fear eternal damnation and still find some measure of relief and hope that Christ has and does forgive them for their sin. The question is while in this condition how can a person know if they have genuine faith, or no? One way to narrow the question further is to apply doctrinal tests. For example, if anyone denies a fundamental doctrine of the gospel, such as that “Christ is God and became man, and who died as an atoning sacrifice for sin". If they are to deny this type of doctrine then their faith is not in Christ as only God could have lived a holy life perfectly under the strict severity of the law and only a man could through blood be a proper sacrifice for human sin. Therefore such a faith could not be genuinely believing in Christ as a means of taking on the punishment of our sin, and no genuine relief could be obtained under the false doctrine.

Every spirit that acknowledges that Jesus Christ has come in the flesh is from God, 3 but every spirit that does not acknowledge Jesus is not from God. (NIV 1 Jn 4:2–3).

Third, a person with faith has the Spirit of God, which means at a minimum they value God above all other things. It is impossible to genuinely believe in hell, one’s proper eternal damnation for the least sin and eternal salvation offered by simple faith in Christ and not secretly value Christ above any other thing. It is not rational to believe Christ and at the same time not value him above all things. Even the weakest believer must value Christ above all or they have never had any faith whatsoever.

We have now narrowed the question to this: For those believers who hold to the primary doctrines of the gospel such as original sin, the trinity, justification by faith in Christ apart from works, etc. and hold him in view as something more valuable then anything else and from fear of eternal damnation find some comfort and relief in his death so that they are not driven to insanity with the otherwise extreme fear that they would rationally hold under their conviction, if they were to fall into various sins, internal or external, how can they know if they have ever had genuine faith, or no?

We now come to a very personal aspect of the question. For outwardly no man would be able to determine who has genuine faith for the confession of the mouth is right, the person seems to have genuine faith, yet they may be not going to church for a long period, may be living in an adulterous relationship, etc. For example there was a member of the Corinthian church that was having sexual relations with his father’s wife (I guess a kind of Mother in law). One would never know if this person had genuine faith but after being excommunicated from the church it turned out that his faith possibly was genuine and he repented of his sin. Yet, here we find another principle. When it is very unclear if a person is a Christian, or not, it is best to assume not and then the fear of hell will drive one back to the comfort and relief of salvation in Christ.

Still, the answer is not sufficient. For many who are backslidden may be so because there faith in Christ is weak and there fear of condemnation great. From this weak faith they stumble into many sins and this only heightens their fear of hell so they try not to think about it. In such a case excommunication and warnings of hell only drive them deeper into despair, so they really need to be reminded of the free grace in Christ and find encouragement to go to him for relief of their fear. In this struggle, to differentiate the condemnation of the Devil who accuses the elect, versus the practical duty of one to encourage their own soul although eternally saved to fear hell more and to encourage ones return back to faith for relief, only the Holy Spirit’s internal witness can distinguish. The fact is that those who have been regenerated by the Holy Ghost as a result of first being justified freely by the grace in Christ, through faith, apart from the works of the law, have an internal witness of the Holy Ghost. Not only so by the Holy Ghost is also the one who preserves correct doctrine in the mind of the believer. (1 John 2:20)

The Spirit you received does not make you slaves, so that you live in fear again; rather, the Spirit you received brought about your adoption to sonship. And by him we cry, “Abba, Father.” 16 The Spirit himself testifies with our spirit that we are God’s children. (NIV Ro 8:15–16)

The conclusion: The elect who have genuinely trusted in Christ receive relief from there dread of eternal damnation and consolation that is never fully destroyed. They therefore persevere and although possibly stumbling into various sins, they never loose that fear of hell and comfort of faith to rescue them from it and therefore return or keep returning to live a life not dominated by the sins they used to commit prior to believing in Christ. During the times when they are down and the conclusion is not clear they are willing to assume the worst and encourage themselves to fear hell in order to arouse their own soul into obedience to faith. However when being accused by the Devil and condemned and so discouraged and fallen into sin through doubt, the Holy Spirit himself will provide assurance so that faith is not snuffed out and a bruised reed not broken, with the final conclusion that the believer will always persevere with faith and be swallowed up in glory forever. Sometimes it is not clear and is not meant to be clear as God himself provides the assurance to the elect ensuring their perseverance.