French term (edited): identité visuelle / sonore

I think this is probably the best pair of adjectives to use — though 'aural identity' is probably a less commonly used term in EN than 'visual...'

I would caution against using 'sound design', as that is a quite specific discipline that is quite a lot more complex. Think of 'aural identity' as being those audio signatures that cohesively identify a particular TV series or series of films — the minute you hear them, you start, even subconsciously, to have an idea where you are. On its simplest level, this can include things like signature tunes, jingles, stings, etc. — analagouse with the corporate logo / type-face / colour scheme one might find in a visual identity.

'Sound design', on the other hand, is the entire soundscape of the film (etc.) — just as we might talk about the 'look' of a particular film, englobing the distinctive work of a particular Director of Photography like say Nick Roeg or Vittorio Storaro. So you can see it is a much broader, and ultimately complex, area.

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Note added at 24 mins (2018-07-29 13:33:35 GMT)
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If you baulk as I did at using 'aural', then I feel you could get away with twisting it to be 'audio'.

I don't think there's any special term in English for "identité visuelle", so it can safely be translated literally.

An "identité sonore", in contrast, is known in several areas of the performing arts as a "leitmotif": https://en.wikipedia.org/wiki/Leitmotif

Although the term has its origins in classical music (think Prokofiev's "Pierre et le loup"), "leitmotif" is also used in the context of film scores to refer to particular themes and harmonies that are "attached" to specific characters (and can be used to make those characters a part of the story even when the actual character is off-screen).

In the case of TV shows, the same idea may be used either to draw viewers' attention on the entire programme (usually known as a "theme tune" marking the start of the programme or its resumption after a commercial break) or to represent individual charcacters, where it is called a "leitmotif" as in the cinema.

Hope it helps.

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Note added at 9 hrs (2018-07-29 22:55:05 GMT)
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For "identité sonore" it should be translate into " similarly audio, sound or tono.

Not my area, but it seems logical to express it this way. Note I am suggesting use of a "/" rather than "-" here.

I think "theme" is a safe choice as it is widely used in descriptions of all art forms, i.e. visual image, sound & music etc.

The two examples below describe "audio/sound" themes and then visual themes respectively.

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Note added at 23 hrs (2018-07-30 12:55:21 GMT)
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"GRAND RUE is strikingly classical in form, yet full of vital human interest. The narrative is based on the principles of titmotif and the musical rondo, whereby the episodes return to their starting, while the VISUAL AND SOUND THEMES are repeated."
https://books.google.co.uk/books?id=m3NgfE9xwmkC&pg=PT145&lp...

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Note added at 23 hrs (2018-07-30 12:56:29 GMT)
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TYPO: The quote in added note should contain "leitmotif", not "titmotif", as I have typed in error.