Couple this with the fact we already knew, from the letter at the poste restante, that there was actually a man in Paris who was passing as Robert Darzac, why did we not immediately fix on Fred himself?
"Of course, his position at the Surete was against us; but when we saw the evident eagerness on his part to find convicting evidence against Darzac, nay, even the passion he displayed in his pursuit of the man, the lie about the cane should have had a new meaning for us.

If you ask why Larsan bought the cane, if he had no intention of manufacturing evidence against Darzac by means of it, the answer is quite simple.

He had been wounded in the hand by Mademoiselle Stangerson, so that the cane was useful to enable him to close his hand in carrying it.

You remember I noticed that he always carried it?
"All these details came back to my mind when I had once fixed on Larsan as the criminal.

But they were too late then to be of any use to me.