I think you are confusing spelling and pronunciation. English has tended to a certain (in some ways confusing) deviation in how different forms of the same root word is pronounced. So:-
In French we have the verb prononcer and the noun prononciation
In English we have the verb pronounce but the noun pronunciation
The French pronounce and spell the syllable in question verb and noun in exactly the corresponding way: the English do not.
So with your word sign, The French pronounce the ‘g’ in ‘signe’ (strictly the ‘g’ and ‘n’ are slurred together as more like ‘ng’) in the same way as in the verb ‘signer’ and the noun ‘signal’ (Latin ‘signum’, probably, it is now thought, pronounced rather like today’s French).
But English, in adopting the word ‘signe’ has shifted its vowel sound from the ‘ee’ to the pronunciation of sign (as in line). Yet in the noun signal this has not happened: the ‘g’ is no longer silent, any more than it is in ‘signify’ (cp. French ‘signifier’, pronounced like ‘signe’). This kind of silent ‘g’ only occurs (as far as I can find) when it occurs in a final syllable (as in ‘resign’ - but ‘resignation’.
Another interesting example is French ‘ligne’, with English ‘line’ (not ‘lign’!). Here the corresponding Latin is not ‘lignum‘ (which means ‘wood’!) but ‘linea’ (meaning ‘thread, or ‘line’, with no ‘g’, silent or otherwise). I do not know why it is not spelled ‘line’ (pronounced ‘feen’) as in ‘fine’ (similarly pronounced). After all, the noun ‘linéarité’ and adjective ‘linéaire’.
Where does that leave us? First, it is an illustration of how language, including how it is pronounced and spelled, over time. A major factor in this, above all in times when literacy was not as widespread and communication was more localised than it came to be by the end of the 18th century, was ‘natural selection’ and, as part of that, what how words sat comfortably in the mouth. One key part of this was the so-called ‘great vowel shift’, in which letters ‘i’ and ‘e’ came to sit higher in the mouth. So, we might think, as ‘ee’ shifted, the ‘g’ before ‘n’ became awkward to say and fell silent. Meanwhile spelling partly sticks with old spelling and partly reacts to the most prevalent changes.
One other point is that it is difficult to speak of a ‘native’ version of ‘English’, or indeed of aboriginal English people. ‘English’ is derived from the language of the germanic tribe of Angles, who invaded, as did the Saxons and then the Vikings, each with their own germanic dialects. Before that had come the Romans, bringing with them people from all over western Europe, the middle East and North Africa. Later, of course, came the French-speaking Normans, whose language filled the aristocracy and, no doubt the legal, medical and merchant professions, as well as Latin-using clerics, while much of the peasantry remained illiterate and had the most passing knowledge of French or Latin. English as we know it emerged from the clash between the two languages. So we see that the words for the most basic things are generally ‘anglo-saxon’ - ‘house’, ‘window’, ‘hand’, ‘where’, ‘go’, ‘foot’, ‘boat’, ‘day’, ‘night’... The French involves things peasants would not possess or need. As the two came together, the Anglo-Saxon tended to prevail for most everyday purposes, while Franco-Latin and, indeed, Greek prevailed for professional, intellectual, technical legal and similar areas of life, of which the large mass of people had little contact. There is no discoverable ‘native’ language. It happened over hundreds of years.
So there is no native English in the sense you mean. The language is a mongrel.