Alain Leroy / Alain Leroy Locke

It is no coincidence that the protagonist "Alain Leroy" in the film is named after the philosopher, Alain Leroy Locke. And you were insightful to catch this.
Btw, where did you happen to find out about this un-renound American philosopher?

The film, Le Feu Fallot (American title, The Fire Within) was made during the french film explosion in the 1960s. The new wave of french directors used "the philosophy of the absurd" (the French existentialist phenomenum that developed after WW2) as a "heady" subject for their filmscripts. These films explore quotidien details of everyday life, e.g., love affairs that end, and try to find a significant meaning in othewise a meaningless existence.

the American Philosopher Alain Leroy Locke was "interested in energy and passion driving the movement" as the motivating force in life. His theory mirrored the idea of Albert Camus, the author of the absurd philosopy novel,_The Stanger_ and book of essays, "The Myth of Sisyphus." Camus also saw life as meaningless, therefore, absurd, in that no matter what one accomplishes in life, man is mortal, dies, and is forgotten. However, Camus agrees with Alain Leroy Locke when he insists that man must "s'engager." That is, man must "engage himself" in order to find meaning for himself in his own life. A man must make himself be motivated by a passion he finds and lose himself in pursuing it; even if he has to convince himself that his goal or purpose is worthwhile. This is the theme of the film "Fire Within" and why the Alain Leroy in the film is named for Alain Leroy Locke, who headed the philosophy about what motivates man.

"The Fire Within" was released by the title, "will-o'-the-wisp" in other English speaking countries. It is the literal translation the french title, Le Feu Fallot. In the online Free Dictionary, the word is defined:

will-o'-the-wisp - an illusion that misleads
ignis fatuus, fancy, phantasy, illusion, fantasy - something many people believe that is false;
2. A delusive or misleading hope.

This is the irony. You absolutely must believe your life is meaningful: in your work, art, or family, etc., even if you have to convince your yourself deep down.

SPOILER ALERT:

In your post, you ask (among other things) about "any 'obvious' philosophical themes/theories explored in the film that a spacker like myself may have failed to pick up on?"

As the previous comment has already addressed the main question in your original post, and some of its tangents, I'll add one observation as to a philosophical theme/theory that I found interesting (if my interpretation of the particular scenes are, in fact, correct, which is up for debate...)

One thing that struck me while watching the film were similarities between two scenes - first, the lunch scene at the clinic, on the day after Alain had been out the previous night with a lover, where the patients at the clinic were dining together for lunch, with two of those at the table engaged in an animated philosophical discussion, with some others at the table reacting to the discussion by ignoring it, others asking to join it, and others having non-related conversations and interactions between themselves. Compare this scene to a scene later in the film, where Alain is with his old friends at a swank dinner party in a fancy home, and politics and philosophy is again being discussed by some of the party goers, with similar reactions among the other guests. In each scene, Alain is more of an observer of the action in the scene, though some of the comments by the other characters in each scene are directed to and/or about Alain, so simultaneously Alain is detached, or a subject/object of the action around him, but in neither scene is he "engaged" with the discussion(s) highlighted in the respective scenes, and, as the earlier comments to this thread have pointed out, the themes of engagement, passion, philosophy, etc., are main elements of the film.

Likewise, and perhaps more significant to me, the two scenes indicated to me that the director was perhaps suggesting that, for Alain, the experience of the two settings (lunch at the clinic, with supposed fellow "sick" people, and dinner with his friends, who, to Alain, have supposedly "made" a success in life in their respective pursuits, a success that Alain feels he has not achieved) were identical in several respects - the expression of self-importance of some of the other characters in each scene, as witnessed and likely disdained by Alain, the relation of Alain to the action in each scene and the other characters in each scene, and the role of Alain in witnessing each scene, which seemed to have a yearning nature to it - wishing he could feel "at home" or "at ease" or "part of" either scenario, yet not feeling so, and, like so many other attempts throughout the film, Alain feels out of place, even though in both places, he's exactly where he "should" be - in the first scene, he's a patient among other patients, and, in the latter scene, he's a "good" friend among other good friends.

Lastly, as in "One Flew Over The Cuckoo's Nest," "Marat/Sade," "King of Hearts," and other films where one of the themes explored has to do with exactly who are the sick people in society and who are the sane ones (and with the theme of what constitutes "sick" and what sanity) the duality of these two scenes in this film (the lunch scene at the clinic, and the swank dinner party at the home of Alain's friends) brought up these same questions for me, in the context of the film, since the characters and action in these two scenes could be seen as interchangeable, and one of the scenes is populated by supposedly "sick" people, while the other scene, very similar in nature and action, is populated by supposedly "successful" people, although this is not at all to suggest that the two categories of people are necessarily exclusive of each other :-)

I just finished watching the film earlier tonite on TCM, and this observation was one of the ones that stuck me most profoundly while/after viewing it. Thanks for the original question, as it gave me the chance to explore my own feelings about it more fully.