What difference does using 'had' make to those two verb tenses, and if so, what is it?

Although these two phrases both appear to use the past tense, the second one actually refers either to the present or the future (but not the past). However, both of them are hypotheticals, referring to events that are not real but imagined. Here is some usage:

If I had studied French, I would be able to read this paper now.

In this scenario, I am holding a paper written in French but thinking about a past attempt (or lack thereof) to learn the language.

If I studied French, I would be able to read this paper now.

This is virtually the same as "If I were now studying French...", meaning that I am thinking about the fact that I am not currently learning the language.

If I studied French, I would be able to live in France.

This is virtually the same as "If I were to begin studying French...", meaning that right now, I don't speak French, and thus can't live in France, but that could change in the future.

I don't know whether these usages are technically actually the subjunctive mood or instead the conditional. However, I can say that it is the presence of the "if" that makes the tenses so strange. Here is how the phrases would look without it:

I had studied French, so I could read papers written in it.

Here, I am narrating a past event (in which I was reading French papers) and describing how, in a time even in the past history of the narration, I studied French.

I studied French for a year, so I can read French papers.

Now I'm speaking in the present and describing how my past study of French helps me read papers now. Note that I had to say something about the duration: the obvious sentence, "I studied French so I can read French papers", actually doesn't scan quite right. There is a similar alternative that does:

I studied French so I could read French papers.

Here, I may be speaking in the present, but I'm not actually reading papers right now. Instead, I'm talking about possibly reading papers: in other words, "I could read" is subjunctive. Note again how the presence of a hypothetical has converted what was a progressive action ("I studied French for a year") into a completed action ("I studied French", period).

They are different tenses. "If I had studied" is the past perfect, and "if I studied" is the simple past. The past perfect, sometimes called the pluperfect, means an event that took place before another event in the past, and generally indicates that that the first event is finished. "If I had studied I would have passed the exam." The simple past does not do so, it simply states something that happened in the past. "If I studied, I will pass the exam." One could not say "If I studied I would have passed the exam".

Simply said

"if I had studied" would be used for your wishful thinking after you've already failed.

"if I studied" would be used for your hopeful thinking before you've sat the exam.