In The Portrait of a Lady, if Isabel was such a clever girl, why couldn't she see that Madame Merle was a phoney?

You are right in a sense. Isabel Archer is presented in
this novel as a bright, articulate and confident young lady. Yet, crucially, she is also
presented as being naive and something of an innocent in her lack of experience, ideas
and sensibilities. We need to remember that in a sense, Madame Merle represents an image
of complete womanhood to Isabel Archer, and therefore Isabel takes her as some kind of
role model. Madame Merle, when she first meets Isabel, is shown to play the piano with
"skill" and "feeling," and we are told that her French background makes her "more
interesting" to Isabel. Note the way that Isabel reacts to her aunt calling her
"secretive":

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Isabel, as a dispassionate witness, had not been
struck with the force of Mrs Touchett's characterisation of her visitor, who had an
expressive, communicative, responseive face, by no means of the sort which, to Isabel's
mind, suggested a secretive disposition. It was a face that told of an amplitude of
nature and of quick and free motions and, though it had no regular beauty, was in the
highest degree engaging and
attaching.

For Isabel who is
trying to work out who she is and what she wants of life, we must understand how Madame
Merle presents an attractive figure and possesses many qualities that Isabel Archer
herself wants to emulate and imitate. Thus, when we focus on how Isabel is presented as
being somewhat naive and unformed through her innocence, we can understand the way that
she is taken in by Madame Merle.