What was Billam's thought process? At first he was going to curse the Jews; after Hashem tells him no, he says 'OK, in that case, let me bless them'? If you want to curse someone, your second option is not to switch up completely and to bless them! What was Billam's real reasoning?
The Sefer Ginzie Yosef gives an amazing answer from Kadmonim It says in the Medrash that why was Rivkah unable to have a child? The Medrash answers so people should not say that Lavan's Bracha came true and therefore she had children. This Illustrates an important point that the *The blessing of a wicked man is really a curse*and now we understand Billam's evil logic he wanted to "BLESS" them which in reality would end up being a curse so Hashem told him NO CAN DO.
Just an added point: Billam was mistaken in his logic. That is by Lavan, Rivkah had not been blessed by Hashem so people would have misconstrued it as his blessing,but in this situation everyone knows Hashem Blessed Klal Yisroel so the Bracha of a wicked man would have done no harm.This explains hashem responce to Billam "For They Are Blessed" that means your trick will not work.
There is no indication that Bilam said any of this of his volition. Rather, the verse (Numbers 22:5), states explicitly:
וַיָּשֶׂם יְהוָה דָּבָר, בְּפִי בִלְעָם; וַיֹּאמֶר שׁוּב אֶל-בָּלָק, וְכֹה תְדַבֵּר
And the LORD put a word in Balaam's mouth, and said: 'Return unto Balak, and thus thou shalt speak.'
The is understood by many commentators to mean that he was forced to say this. For example, Midrash Aggada (Buber: 23:5) states:
בעל כרחו שלא בטובתו בקש לו לילך לדרכו
See also Ramban.
Regardless of the degree of coercion, the overwhelming implication is that the above verse was, at least in part, the impetus for Bilam's behaviour.