Does English have digraph GN that does not come from Norman (Old French)?

Old English had a lot of words spelled with "gn" somewhere in the word. With some patience you can get a pretty complete list on Bosworth Toller's Anglo-Saxon Dictionary online by doing a regular expression search for gn (the first 500ish hits are valid, the rest match words found in the body of the definition).

Cross checking with the OED, I see that very few current words have an etymology of "germanic" and are spelled still with a "gn" (most of them I've never heard of and were added to the language from German itself much later). The two I have heard of are "gnat" and "gnaw", which both date back to Old English. One I haven't heard of is "agnail" (OE angnægl,), which according to the OED is etymologically from "the Germanic base of ange + the Germanic base of nail" (see also Etymonline).

I do see there are plenty of words that are still used that lost the "gn". For example, "again" was once spelled ongeagn. In addition, "rain" was spelled regn.

At the start of words like gnaw

Yes, at the start of some words like gnaw. Even though the G in gnaw is “silent” in present-day English, it used to represent a consonant sound. So originally, the "GN" in this word wouldn't have been a "digraph" so much as a consonant cluster (albeit a special kind of consonant cluster: the sounds are "tautosyllabic" or in the same syllable). As the spelling suggests, the consonant cluster is thought to have originally been pronounced as [gn], although it may have developed other realizations in certain time periods.

The distinction in pronunciation between words starting with gn- and words starting with n- seems to have been lost sometime in the early Modern English time period (An Introduction to Early Modern English, by Terttu Nevalainen (2006), says the change of gn- to /n/ was "completed in the south in the eighteenth century", p. 128).

In the middle of some compound words like hangnail

There are also some compound words made from native elements that are spelled with -gn-, such as hangnail.

"G" itself isn't very frequent in non-word-initial position in native English vocabulary because of sound changes

The /g/ sound is a bit rare outside of word-initial position in native English vocabulary because it was historically vocalized in many contexts to /j/ or /w/.

The vocalization of G to /j/ (in palatalizing contexts) had already occurred by the time of Old English (at least, in West Saxon dialects), so the letter "G" in Old English spellings could represent the palatal glide /j/ (we have evidence for this from spellings that use G unetymologically to represent /j/ that did not originate from the Proto-Germanic *g sound; e.g. the word for year, cognate to German Jahr, was spelled with the letter G in old English). The Old English word regn that Laurel's answer mentions was probably pronounced something like /rejn/.

The vocalization of G to /w/, which occurred later, seems to have developed via rounding of earlier /ɣ/. An example is the Modern English word owner which the OED says had spellings like agenere, agnere, and ahnere in Old English. The Bosworth-Toller entry is at ágnere.

The pronunciation of "-gn-" as /gn/ is not inconsistent with Latin, or even French origins for a word

The pronunciation of -gn- as /gn/ in many Latinate words is based on spelling (and also partly on certain traditions for pronouncing Latin, which may have themselves have been based on spelling): it doesn't have much if anything to do with Germanic. Note that even though -gn- is pronounced as /ɲ/ most of the time in French words, there are actually some learned French words where /gn/ is used, such as ignition and stagnation.

Other words of English etymology using "gn" are gnarl, gnash, and gnat. As sumelic has pointed out, they are found at the beginning of these words.

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.