According to my textbook, when fluorine reacts with water, it produces oxygen and ozone.
\begin{align} \ce{3F2 + 3H2O &-> 6HF + O3}\\ \ce{2F2 + 2H2O &-> 4HF + O2} \end{align}
Is hydrogen peroxide ($\ce{H2O2}$) produced under any conditions on reaction of fluorine with water?
Answer
No, Hydrogen Peroxide is not produced under any conditions on reaction of fluorine with water. Fluorine is such a strong oxidizing agent that it even oxidize water to oxygen and ozone by ripping apart hydrogen bond from water and bonding with fluorine to form hydrofluoric acid. The reaction of water and fluorine can be found here and here. Yield of ozone is less than oxygen and can be considered as an impurity. Apart from oxygen and ozone, atomic oxygen is also produced.
$$\ce{F2 + H2O → 2HF + [O]}$$
If you use ice cold water, very minute amount of hypofluorous acid($\ce{HOF}$) is also formed which is present in solution in equilibrium.
$$\ce{F2 + H2O ⇄ HFO + HF}$$
Reaction between fluorine and water to form hypofluorous acid and hydrogen fluoride. The reaction proceeds at a temperature of -40 ° C. The reaction is conducted M. Studer and E. Eplamenu in 1971, the first time obtaining hypofluorous acid (by fluorination of ice.(Source)
Hypofluorous is very unstable compound as it readily disproportionates into $\ce{HF, F2}$ or $\ce{H2O}$. As such it has not been isolated yet as a solid compound.
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