The entire Psalm 14 reads:
"The fool hath said in his heart, There is no God. They are corrupt, they have done abominable works, there is none that doeth good. The Lord looked down from heaven upon the children of men, to see if there were any that did understand, and seek God. They are all gone aside, they are all together become filthy: there is none that doeth good, no, not one. Have all the workers of iniquity no knowledge? who eat up my people as they eat bread, and call not upon the Lord. There were they in great fear: for God is in the generation of the righteous. Ye have shamed the counsel of the poor, because the Lord is his refuge. Oh that the salvation of Israel were come out of Zion! when the Lord bringeth back the captivity of his people, Jacob shall rejoice, and Israel shall be glad."
So the possible interpretations are, this is explaining that people who say there is no god are fools, and none of them do good...or that these specific people, none of which do good, and who say there is no God, are fools. If you say that the first is correct, and use it as justification that atheists are fools, then you have the problem of the falsity of the statement that no atheists do good. "There is none that doeth good, not one." All the secular humanists helping the hungry and sick and caring for humanity as a whole pretty clearly proves that there are atheists who do good. That only leaves you with the second interpretation. Or the Bible being wrong, but I know you don't think that.
The text clearly says that "fools say (in their hearts) that there is no god" rather than "Those who say (in their hearts) that there is no god are fools". However, it makes sense to consider it both ways. The text describes fools more explicitly than atheists.
Remembrance of god does not reside in their hearts. They may not claim to be atheists with their mouths. For many centuries, professed atheism was a rare position. If they once possessed any knowledge of god, these did not retain it for consideration in their hearts. The fool denied god in his (or her) heart and motives.
In the Proverbs 1, Solomon, that teacher upon wisdom, asserts that fools hate wisdom and instruction (v.7) and that fools hate knowledge (v.22).
I will give credit to the professing atheists here that they don't hate all knowledge.
But, what might be the motive for retaining no acknowledgment of God? God knows motives but it is possible that some don't want there to be a god. If God exists, that means that there could be potential consequences after death for sinfulness that encountered no consequences on earth.
At the conclusion of the Sermon on the Mount, Jesus commended the ones who would hear the saying of Jesus and do them as being like the
wise man who built his house upon the rock. He added:
"And every one who hears these sayings of mine and does them not shall be like a foolish man who built his house upon the sand" (Matthew 7:26).
Earlier in the Sermon, Jesus had spoken the lines described as the "Beatitudes":
Blessed are the pure in heart: for they shall see God (Matthew 5:8). Exhortation: hear and do and you will see.
My observations here and elsewhere are that atheists can be very intelligent and disciplined. Some heart attitudes apparently do not consider God when pondering an action. Other heart attitudes fear God and behave accordingly. Heart attitudes can be expected to have an impact on morality. But, human hearts are impossible for all but God to know and understand accurately (Jeremiah 17:9). Emotions and intuitions can drive us. Sometimes, it is difficult to even understand ourselves.
The text of Psalm 14 is largely repeated with seemingly minor variations in Psalm 53. Mankind is generally depraved rather than generally good although many noble deeds do happen. There is none who does good as he or she should nor any who seek God as He ought to be sought.