Well, I hesitated for a while before commenting on this song because I think people do need to have a certain background to understand and accept that, sometimes, there might be much more to a song than what appears at first glance. Let me try to give my interpretation and see how it flies...
BTW, a few lines are not quite right in the English translation and it is important to keep that in mind.
Gainsbourg’s lyrics are just like MF lyrics; they can be read and interpreted in different ways (at different levels) and many of the songs written by those two have a deeper (or occult) meaning that could be considered as being controversial and/or disturbing. Concerning this particular song, I would say that most people would interpret it as being about a woman who asks a lover to tell a second lover (a person that will be shattered by the revelation) that she is in love solely with the former. The problem with this superficial analysis is that many lines don’t make sense at all. But there is another interpretation.
The most enigmatic lines refer to “programming” and a “double”. There are two concepts that one most take into account if one is to be able to decipher the lyrics; mind control and dissociative disorders. Myself, I think this song is about a woman facing an internal conflict caused by her multiple personalities. Those personalities seem to have been created by a sort of programming, or “mind control”. These themes are quite ubiquitous in popular music today, but anyone initiated will know that they have been used for decades. Gainsbourg is a master at this sort of game where lyrics will be quite efficient at conveying both a superficial and a deeper, occult layer. In this case, basically, the two lovers (two men) are, in fact, two alters (two doubles). A particular line that will seem meaningless to most is “Questions de pleins et de déliés” which is translated literally in the English version. In French “pleins” and “déliés” refer to the thick and a thin strokes in calligraphy. One could interpret this as being the two states, or the two sides of a letter, or a person. Also, interestingly, the song “Tandem”, which is taken from the same album, seems to be a variation on the same theme (“Variations sur le même t'aime”)!
This is yet one possible interpretation of this song and, evidently, anyone can claim that this is all speculations and that Gainsbourg never intended to give it that meaning. I would say that one has to have at least some knowledge of occult concepts concealed in popular art to be able to present an informed opinion on such topics.