Ages ago someone told me that most readers will not spot a double-the in a sentence. Something about the way we process words apparently filters out the extraneous "the" but I don't know what that process is called. Does it have an explicit term? What is it?
This is referred to here and numerous other places as "top-down vs. bottom-up" processing, and is a cognitive error rather than a visual one - that is, the illusion is caused by filtering of the material seen to match expectations as opposed to a true visual illusion, which exploits faulty visual processing.
The original illusion is stronger than it is in the title here because the phrase is broken across lines:
PARIS IN THE
On a quick glance, the "top-down" processing matches the sentence against similar phrases familiar to the reader, and results in a match to "PARIS IN THE SPRING", and the perception that this is what is there. In contrast, if the reader specifically reads each word separately -- "bottom-up" processing -- they look at one word at a time, and see
PARIS IN THE THE SPRING
thereby detecting the duplicate "THE".
It's probably reasonable to to say that it is a facet of inattention blindness.
It's a factor of how our minds filter stimuli for consumption.
I don't know if there is a more specific term that applies.