The French have very effective forces and they have been, and are still being, deployed operationally. They have an extensive record of operations in various Francophone regions of Africa. They exercise frequently with NATO forces and are the lead country in major projects such as NATO ACCS.
However.
They have their own agenda. They wanted an integrated EU military force, and undoubtedly still do. I have no doubts they would insist on several of the higher ranking NATO posts and would campaign to make it a more European force and to supplant the USA as the lead nation on many projects and technology programmes.
I see no need to upset the applecart. I can see no major problems within NATO or with the current means of coordinating their forces which would require their entry, whilst I can see many potential problems subsequent to their entry.
If it ain't broke - don't fix it.