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I heard, in the case of the French language, the French Academy decides whether a newly coined or imported word can be accepted as a part of the standard French. In the case of English, there is not such an institute authorized by a state or states where English is spoken. Only what we can know is whether editorial boards of great dictionaries like Oxford English Dictionary (for BrE) and Webster (for AmE) have admitted the entry of a newly coined/imported word in their dictionaries.
Speaking about "estimable", its entry is admitted both by OED and Webster. The origin of the word is Latin "aestimabilis" and the first use in English was documented as early as in 15 century. Generally speaking, in the words of the form "X-able", the "X" is usually a verb and the meaning is "be-able-to-X". So the word "estimable" is "be-able-to-esteem". Suppose "approximable" is to be accepted as a good English word, then there should be a verb like "approxim". Have you ever come across such a sentence as "The radius of the Earth was approximed to be 6350 km"? I guess the absence of "approxim" in English is the reason why editors of OED or Webster are still disapproving the entry of "approximable". Nevertheless some knowledgeable people use it because they know there is a verb "approximare" in Latin. The English word "approximate" was at first accepted only as an adjective because this came from the Latin "approximatus" which is the past participle of "approximare". So to say "approximatabe" is like to say "writtenable" or "spokenable". I guess the reason why "approximatable" is not accepted as an English word is that the editors know that "approximate" is an adjective in its proper nature.
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