What is a false crocodile?
If you keep reading the next sentence it makes clear what is meant (emphasis mine):


  Crocodiles (subfamily Crocodylinae) or true crocodiles are large semiaquatic reptiles that live throughout the tropics in Africa, Asia, the Americas and Australia. Crocodylinae, all of whose members are considered true crocodiles, is classified as a biological subfamily. A broader sense of the term crocodile, Crocodylidae that includes Tomistoma, is not used in this article


So, the Crocodylidae family refers to crocodiles, the Crocodylinae subfamily are the true crocodiles which includes almost everything known as a crocodile, and indeed, you found the one that gets left out:


  The crocodylian family Crocodylidae includes the true crocodiles, which are the members of the subfamily Crocodylinae, as well as potentially the false gharial, the only extant member of the subfamily Tomistominae. The latter is a subject of controversy as to whether it is a crocodile or actually belongs in the family Gavialidae.


(via Wikipedia)

Wikipedia further states:


  Gavialidae have conventionally consisted of only one surviving species, the gharial (Gavialis gangeticus), which is native to India and Nepal. Many extinct species are also known


and also


  Tomistominae is a subfamily of crocodylians that includes one living species, the false gharial. Many more extinct species are known, extending the range of the subfamily back to the Eocene epoch. In contrast to the false gharial, which is a freshwater species that lives only in southeast Asia, extinct tomistomines had a global distribution and lived in estuaries and along coastlines.


So there are many other extinct relatives of crocodiles in these groups; the question is to which the extant false gharial belongs. In either case, the other Tomistominae would be non-true crocodiles, according to a definition that subfamily Crocodylinae are the true crocodiles.

The words "true" and "false" are not necessarily used in their boolean meaning here, but rather, "true" in taxonomy fits better with other definitions, for example from Merriam-Webster: "typical" (Merriam-Webster explicitly references the "true cats" as a use for this meaning). A synonym would be more like "archetypal" or refer to a clade or other more robust grouping, rather than a linguistic/non-scientific grouping.