Could more French warships have joined the Free French?

Were there realistic ways for more of the French Navy to join the Free French or other Allied navies in 1940?

Yes, especially for ships already in Allied ports, but political defeatism and the choices of the Vichy government sharply limited those possibilities.

Ships already in British or British-held ports had the clearest opportunity to join the Free French, while the choices presented at Mers-el-Kebir created other possible paths. Those alternatives cannot be separated from the French government's defeatism and the political trauma left by the First World War. The decision to seek an armistice belonged to the government; French servicemen and civilians could still choose to resist.