Montag is happy when the book begins, but he is not at ease; because of his internal confusion over the purpose of burning books, he only takes superficial joy in his job.
He walked toward the comer, thinking little at all about nothing in particular. Before he reached the corner, however, he slowed as if a wind had sprung up from nowhere, as if someone hadcalled his name.
(Bradbury, Fahrenheit 451, Google Books)
Montag clearly takes great pride and joy in his job, but every word is tinged with doubt; his "fierce smile" remains on his face after burning the books, but this is not necessarily from his own internal joy, instead being an instinctive reaction bred into him by society. It is clear, as he loses his elation just by walking away, that he is not fully happy, even though he does not yet understand his dissatisfaction with society.
Montag is not content in the beginning of the book. He feels unsettled about his life but does not understand why. This discontent with his day to day life is part of what allows him to see problems in the world around him and leads to the development of his personal conflict within the novel. This is waht allows him to be troubled by the young neighbor girl as well. He thinks he is happy, and he believes he is living the perfect life because he is told so by the barrage of images and sounds he is constantly processing. He assumes he is happy, but does not truly understand what happiness is until much later. It just takes someone asking him if he is happy for him to finally question that reality.