seepage through French drains
In my experience, a french drain is placed just below the ground surface outside the house to attempt to provide surface water a way to run off before finding it's way down to the foundation, where you report problems on the inside.
With a hunidity level of 60% it could easily be a condensation problem. Indoor humidity should be no more than 40%. That is a level that is healthy for people but a house is happier at 15-20%.
To test, take a piece of plastic about two feet square and use duct tape to seal it down to the concrete floor for a few days.
If you find moisture under the plastice, between it and the crete, then the moisture is coming from still curing concrete or from water under the slab. If the moisture is found on top of the plastic, it is surely from condensation.
I am also not sure what is meant about meeting of new and old concrete. Is this just a patch where the old was cut out for drain material or was a whole new slab poured? Was a 3 or 4" perforated drain laid into stone under the slab? Was a vapour barrier used before the slab was poured? This picture is incompleete.