I agree that Pearson looks better, particularly on the Scale Independence plot.
Also, from the module-trait graph I obtain certain Pvalues associated
to each module and some of them are lower than 0.05. However if I
adjust the Pvalue by bonferroni (or any other method) and the total
number of modules, none of them becomes significant. Does it mean my
data is useless? Can I use in further analysis the modules that are
significantly associated to any of the traits with uncorrected
It does not mean that your data is useless. We faced the same issue using WGCNA in the lab in Boston (USA). We were eventually able to publish the data with the nominal (unadjusted) P values. Bonferroni correction is the most stringent P value adjustment, though - why not try with Benjamini-Hochberg?
I want to check for TF associated to the genes in each module to look
for regulators of the associated traits (fecundity and lifespan).
Should I modify any parameter to make them most significant?
You could modify the tree cut height, which will affect the final number of modules, which, in turn, will affect the P value adjustment. You can also filter out genes before performing WGCNA, like genes of low expression and/or genes of high variance.