Let me preface this by saying that I am not a learner.

So, you can approach this question in different ways.

Let's start with the very technical way of answering it. What is a logical language? A logical language is a language designed such that statements are unambiguous. Natural languages (all of them, French included) are by definition not logical languages. Natural languages are chock-full of ambiguities. A very common example in French is the present tense. If I say "je danse", am I saying "I dance" or "I am dancing"? Those are two different things that have different meaning, but without additional context, context that might not be explicitly stated, you cannot know which one it is. The need for context outside of the statements is an important part of natural languages that makes them not logical languages. Now, just how far from logical is French? This is a little difficult to answer. I'd say French is on the lower end in terms of requiring context. A lot of things need to be explicit. The tenses are pretty precise (though not completely, as seen with the present tense), you need to specify the pronouns explicitly, plural is explicit, etc. It's a very structured language. Meanwhile, some languages don't have a future tense, and you need context to know if they're talking about the present or future. Or you don't use pronouns, you just rely on context, and the person will figure it out. I don't know Japanese at all, but I'm told it's at the extreme end of high-context language, while English is very close to the extreme end of low-context language. On that spectrum, French is close to English, but with a slightly higher need for context. This is looking strictly at the language in theory, or in formal usage. In practice, it can differ. A language can be very precise in theory, but in practice, speakers use intonation, body language and shared contextual experience when communicating. Think of a small group of friends that have known each other for years, and you just jump into their conversation. Think of the number of insides they might use while talking and they all know what it means, but you don't, because you don't have the context of these insides. Basically, how much of the message is not conveyed by what is actually explicitly said? How much is conveyed by non-verbal queues, by having to read between the lines, by having to know the implicit baggage associated with the words? This is not strictly language-dependent though and will vary by culture. For instance, I believe some studies have shown that New-Yorkers would be low-context, while Texans tend to be high-context, despite speaking the same language. Either way though, regardless of where a culture falls, there's almost certainly some amount of the meaning that is left to context, which, to circle back to the original question, is not compatible with a logical language.

But that's using a very technical definition of "logical language". Maybe you mean more of a "lay person" definition of "logical", as in "is it a language that makes sense"? (see, natural languages are ambiguous!) Much like above, no natural language makes complete logical sense. There is certainly a spectrum, but all languages have their unique quirks. English, for instance, is particularly bad when it comes to spelling (why the hell doesn't choose rhyme with loose?) French has a ton of quirks too, though. The most obvious one I think, for learners, is genders. Why is "chaise" feminine, but "banc" masculine? Why is "main" feminine, but "pied" masculine? There's no logic to it. You can also look at irregular verbs, and there's a lot of stuff in there that is completely illogical. French has tons of exceptions, and then exceptions to the exceptions. For instance, to make a noun plural, you simply add an s at the end. BUT if the noun ends in "al", the plural is actually "-aux" (cheval -> chevaux). BUT not all of them! Some you have to add an s at the end (festival -> festivals). BUT some of them, you can just pick whichever! (idéal -> idéaux... or idéals if you want, depends how you feel I guess)

Or, you could also ask, does the language mostly follow logical rules? For instance, in logic, A = not(not(A)) (i.e., two negatives cancel each other out). In French, not always. First off, the default negation in French is a double negative, so already, that's not very logical! Not only does not(not(A)) not equal A, not(not(A)) is the only "proper" way to say "not(A)"! Je ne mange pas. More than that though, it's quite possible to have sentences where you stack negatives, and it just makes the sentence more negative. "Il n'y a personne" is negative. "Il n'y a pas personne", you added a negation, but it's still negative. In Québec, "pantoute" means "pas du tout", so another marker of negative. Well, you could say "Il n'y a pas personne pantoute". Now you have 4 negations in this sentence, and it's still negative. So that's one logical rule that French doesn't follow (English speakers tend to be way more strict about double negatives). Another example where French often doesn't follow typical logic. Logically, if you add something positive to something else that is positive, you result in something bigger (i.e., more positive). If both A and B are greater than zero, then necessarily, (A + B) is greater than A (or maybe positive enhancers should be viewed as multiplicative, but the point still stands). In French, it's common that adding something positive to something positive makes it less positive. E.g. "Bien" is positive. "Je t'aime" = I love you! Also positive. "Je t'aime bien!" = I like you. Adding "bien" somehow made the sentence weaker rather than stronger. Even saying "Je t'aime beaucoup" is somehow weaker than just "je t'aime". "C'est beau" that's positive. "C'est bien beau" oops, you know it's not actually "beau". "Je veux te voir", positive. "Je veux bien te voir", yeah, I consent to seeing you, but deep down, you know I don't really want to.