I have to amend my earlier statement about the butterflies of leaving the Fuzhou shipyards undamaged. I had neglected the fact that during the Sino-Japanese War, the navies from the southern Chinese provinces only offered minimal support to the Beiyang navy; so even if they had more ships it wouldn't have made a difference. The military structure of Qing China was so decentralized that even when the country was at war, some provinces could unilaterally declare themselves noncombatant and keep their forces idle; this happened both in the Sino-French war and the Sino-Japanese one.
However, if in TTL the Sino-French war is averted, Li Hongzhang, as Viceroy of Zhili, might convince the commander of the Nanyang navy--who due to the butterflies from ships not getting sunk and whatnot may not be the same man as in OTL--to send him reinforcements. But then again that isn't a necessary consequence, just a possibility. I'll have to give this some more thought.