In the story, "The Jewels," what does Mr. Lantin realize about the "fake" jewelry his wife owned?

In this darkly humorous tale Monsieur Lantin, after the
death of his seemingly devoted and loving wife, discovers that appearances can be very
deceiving and that you cannot judge a book by its cover. Reduced into penury following
the death of his wife, Monsieur Lantin decides to sell some of his wife's
fake jewellery to gain some extra money. It is when he takes a large necklace to a shop
that he finds out the truth:

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Monsieur Lantin, embarrassed by all this ritual,
was opening his mouth to say: "Oh, I know perfectly well that it isn't worth anything,"
when the jeweller said: "Monsiuer, this necklace is worth between twelve and fifteen
thousand francs; but I couldn't buy it unless you told me where it came
from."

Clearly, the jeweller
suspects him of having robbed the necklace. It is when he takes it to another jeweller
to be valued that the truth is made clear. As Monsiuer Lantin wanders away completely
shocked at the value of the necklace, he asks
himself:

He
tried to think it out, to understand. His wife couldn't have afforded to buy something
so valuable - that was certain. But in that case it was a present! A present! But a
present from whom? And why was it given
her?

What is never actually
stated but is strongly hinted at is that these "presents" were from a wealthy lover -
Madame Lantin had been having an affair with a wealthy gentleman, who had given her
these jewels as a gift.