Thanks everybody for your suggestions. I’ve solved my problem 
In fact, the culprit was (once again) Murphy. But this time, the Murphy’s rule worked in reverse : it made something work although it should not.
More clearly now 
As suggested, I’ve tried outside, and then the GPS generated valid coordinates after a handful of seconds only. So it is still working fine, and it was a problem of signal quality.
What sent me on the wrong direction is the fact that, despite it was in my workshop inside the house, it worked fine the first time I tried it, although it shouldn’t. So when it didn’t work during my latest experiments, I was not thinking at all it could be the problem.
Best regards and thanks again.
Eric