What is Food color ?

To identify the mechanism of a detection process, you have to theorize the behavior of our probe depending of the different models. This includes the prediction of behavior of your probe in conditions that you have still not tested. A successful prediction will offer you plenty of confidence.

Spectroscopic evidences are part of the job. And, as you mentioned, a change in the fluorescence spectrum is not predicted by FRET or PET.

Quantitative measurements offer also pieces of evidence. The quenching efficiency can be calculated in the case of FRET and partially calculated for PET.

An example of quatitative analysis of fluorescence quenching experiment was discussed in “Can anyone help me to do stern volmer plot in flourescence quenching?” at

https://www.researchgate.net/post/Can_anyone_help_me_to_do_stern_volmer_plot_in_flourescence_quenching

If you are getting a considerable overlap zone of absorption of acceptor and the emission of the donor then the FRET efficiency can be calculated. Nothing wrong with the calculation of different parameters to come to conclusion. Even the same can be calculated after the addition of the analytes.

-You wrote, "a blue shift in the emission spectrum upon the addition of the analyte." This means your probe is already fluorescent and upon interaction with the analyte, it shows a blue shift. This suggests some charge transfer mechanism is working.

-In PET you can see on-off or vice versa responses at the same wavelength. That does not seem your case.

-You wrote, "I got good overlap with UV of analyte and emission of the probe."

For FRET, the donor emission must overlap with the acceptor absorption. That means, upon excitation of the donor, you should observe the emission from the acceptor. You can perform studies to check your system. You can look up some review articles to understand the FRET mechanism:

(PDF) Resonance energy transfer-based fluorescent probes for Hg 2+ , Cu 2+ and Fe 2+ /Fe 3+ ions (researchgate.net)