Saul was given to Israel as a permissive will of God when they asked for a Samuel for a king. They were therefore given a king of their choice.
1 Samuel 10:19
19 And ye have this day rejected your God, who himself saved you out of all your adversities and your tribulations; and ye have said unto him, Nay, but set a king over us. Now therefore present yourselves before the LORD by your tribes, and by your thousands.
Yet God by foreknowledge knew this was going to happen for he said by Moses:
14 When thou art come unto the land which the LORD thy God giveth thee, and shalt possess it, and shalt dwell therein, and shalt say, I will set a king over me, like as all the nations that are about me;
15 Thou shalt in any wise set him king over thee, whom the LORD thy God shall choose: one from among thy brethren shalt thou set king over thee: thou mayest not set a stranger over thee, which is not thy brother.
God at the very beginning had his choice of a king from the tribe of Judah. For he had prophesied of the Kingship of Judah:
10 The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be.
His chosen king from the beginning was Shiloh, but until He came Judah occupied his seat. Saul had to fail for the predestined purpose of God to take effect:
1 Samuel 16:1
1 And the LORD said unto Samuel, How long wilt thou mourn for Saul, seeing I have rejected him from reigning over Israel? fill thine horn with oil, and go, I will send thee to Jesse the Bethlehemite: for I have provided me a king among his sons.
Out of the lineage of Jesse, His king was going to come, the messiah, to whom dominion and honour belongs.
There is the permissive will of God and his perfect will. God does not repent doing his perfect will, but his permissive will makes a way for his perfect will. Saul had to fail in order for the perfect plan of God to be made manifest through the lineage of David. God repented making Saul a king because he was not his choice from the beginning, he was man's choice of a king.