What is the advantage of adversary if the random number repeats? In proof of CPA-security of encryption scheme $(r, F_k(r)\oplus m )$
where:

$F_k$ is a keyed function
$r\in_R\{0,1\}^n$ is a random number,
on page 85 of Introduction to modern cryptography we have


The value $r^*$ is used when answering at least one of A’s encryption oracle queries: In this case, A may easily determine whether $m_0$ or $m_1$
was encrypted. This is so because if the encryption oracle ever returns
a ciphertext $\langle r^*,s \rangle$, si in response to a request to encrypt the message $m$,
the adversary learns that $f(r^*) = s\oplus m.$


My question is how can the adversary use $f(r^*)$?
Haven't we assume that the adversary doesn't know about $f$?

What I understand is that if we have used the keyed function $F_k$, then since the adversary doesn't know $k$, the knowledge of $F_k(r^*)$ can't be used because s/he still needs lots of time, that is $2^{|k|}$, to check which function $F_k$ where used. So it seems to me using the encryption scheme is secure even we repeat the random number $r$.
It seems that I am missing something but I can't find it.
Thanks to @fgrieu I've got the point I've missed.
The point is the adversary doesn't want to find the keyed function, of course, s/he would be happy if knew it, but s/he wants information and wins some game.
So Let's think like an adversary and we have asked $z$ queries $m_1, \cdots, m_z$ and got $\langle r_1, F_k(r_1)\oplus m_1\rangle, \cdots , \langle r_z, F_k(r_z)\oplus m_z\rangle$. We can have the following information from the queries' answers.
$F_k(r_1) = F_k(r_1) \oplus m_1 \oplus m_1$
$\vdots$
$F_k(r_z) = F_k(r_z) \oplus m_z \oplus m_z$
Then we choose $m'$ and $m''$ and get one more ciphertext $F_k(r')\oplus m_b$. If random number r repeats, for example r'= r_i, then we can do the following computation
$F_k(r_i)\oplus m_i \oplus m_i \oplus F_k(r') \oplus m_b = m_b$
And we exactly know which message was encrypted just by checking whether $m_b = m'$ or $m_b=m''$.
Even the adversary still doesn't know the $F_k$ we used he win CPA-game.