Not necessarily. In reality, modern systems use the Unicode Bidirectional Algorithm (BiDi) to properly mix LTR (French, English) and RTL (Arabic) text.
Some examples:
LTR (French) interface: The French text is displayed normally. The Arabic passages are displayed from right to left within the text. This is often the best choice if the document is mostly in French.
RTL (Arabic) interface: The Arabic is displayed naturally, but the French segments can sometimes appear out of place, especially when there is punctuation, numbers, parentheses, or URLs.
Mixed Arabic/French text: This is where the problems arise. For example:
The message is (مرحبا بكم) today.
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or
Request number 12345 is confirmed.
رقم الطلب 12345 est confirmé.
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Punctuation and visual order can become confusing depending on the browser, application, or font used.
Therefore:
If your goal is to understand the content, translating all the text into French completely eliminates the problem.
If you need to keep both languages, it is generally not recommended to switch the entire browser to RTL. It is better to keep the interface in the document's primary language and let Unicode handle the Arabic portions.
From a technical standpoint, RTL doesn't "break" French, but it can alter the visual order of some mixed elements (commas, parentheses, numbers, web links), which can give the impression that the text is displayed incorrectly even though the characters themselves are correct.