If the Father is the "only true God" (John 17:3), does that mean that Jesus is a false god?

Only the Father IS the "true God". The entire context of the verse where Jesus begins praying to the FATHER starting with John 17:1 needs to be considered.

At John 17:1, 3 Jesus prays to the Father: "FATHER, .... this is eternal life: that they may know you, the only true God, and Jesus Christ whom you have sent." - New International Version (NIV). Here the Father alone is not only very clearly identified as the only true God, but Jesus Christ is again pointedly and specifically excluded from that identification ("AND Jesus Christ whom YOU [the only true God] have sent").

For God to be mentioned as the "true" God does not demand that all others called `god' or `gods' are false gods. The inspired scriptures when speaking of faithful angels, prophets, God-appointed judges, kings, and magistrates clearly calls them "gods" on occasion. These are called "gods" in the sense of faithful servants of God, representing the true God.

If we should see, for example, someone being called the `true prophet', that should mean that the person so described is truly a prophet. In either case this certainly does not have to mean that all other prophets must be false. Even if it was said that this one was the "only true Prophet," we would probably consider him the only prophet in the HIGHEST of the word, but that still would not make ALL other prophets of God FALSE prophets.

So, the title "the true God" does not have to mean that there are no others who may be called "gods" or "a god" in a subordinate but righteous sense. It is, however, an exclusive title for God, the Most High, only true God, Jehovah. And clearly it refers exclusively to the Father. No one else is the God or the True God. (Ps. 86:10; 2 Kings 19:19; Is. 37:16.)

For more, see
God and gods - What is a god and who have been 'gods'?

Is There Only One True God?
 
WHO IS “the Only True God”?
 
Identifying the Only True God
 
“Those Who Are Called ‘Gods’”