Yes, the two (or more) gospel view is false.
It is also known as Mid Acts Dispensationalism (a.k.a. MAD).
MAD in certain circles teaches that there is one gospel by Jesus and another gospel by Paul.
However, Paul was a Jew. So if he was a Jew, then why would he teach that which did not apply to him? Also, why did Paul write to other Jews if he was supposed to only write to the Gentiles?
For Peter says that his beloved brother Paul had also had written unto of whom Peter was writing to, as well.
"And account that the longsuffering of our Lord is salvation; even as
our beloved brother Paul also according to the wisdom given unto
him hath written unto you; As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction." (
2 Peter 3:15-16).
In addition, ...
What was Paul's opinion regarding the teachings or words of Jesus Christ?
“
Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world,
and not after Christ.”
(
Colossians 2:8).
“
If any man teach otherwise, and consent not to wholesome words, even the words of our Lord Jesus Christ, and to the doctrine which is according to godliness; He is proud, knowing nothing, but doting about questions and strifes of words, whereof cometh envy, strife, railings, evil surmisings, Perverse disputings of men of corrupt minds, and destitute of the truth, supposing that gain is godliness: from such withdraw thyself.”
(
1 Timothy 6:3-5).
So Jesus and Paul taught the same gospel or teaching.
In fact, Mid Acts Dispensationalism is nothing new. Back in Paul's day, people were also wrongfully following Paul, too. For Paul said that there should not be divisions between Christ and what he taught (1 Corinthians 1:10-13); For Paul said, "Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul?" (1 Corinthians 1:13).
For Paul said, if any man preaches another gospel, let him be accursed (Galatians 1:6-9). Soooo... if Peter or Jesus was preaching another gospel different than Paul's gospel, does that mean that they were accursed? No, of course not because it was all the same gospel.