Going straight from nat 5 french to advanced higher?

I plan to take advanced higher maths, physics, computing science and higher french. However, due to the lack of pupils picking advanced higher computing science as an option, I might not be able to take it. I'm applying to Cambridge next year so I need 3 advanced highers, so I was thinking about jumping straight to advanced higher french, having only done it at nat 5 level before?

For background information, I excelled at nat 5 french - winning the award for the best in the year at it and achieving an A1. Unfortunately I couldn't take it in 5th year because of how the timetables worked out. Is the jump from higher to advanced higher really that big? If I had to, would it be difficult for me to just do advanced higher in 6th year having only done national 5 French in 4th year?

The jump from AH from H is big. N5 to H is not that big of a gap, but H to AH is. I did H in a few months, using skills I'd developed over the time of my 1 and a half N5 years, but with AH, there is a gap. I did get an A, but it takes time to develop the language level necess. By the end of AH, you'd have a B1 or B2 level, which is hard to develop from N5, like A1/low A2, but, arguably, maybe doable. This would need a lot of dedication over the summer, as you'd need to be at a level for reading French books for your diss. You could also argue that it may take you that time to just get back to the level, depending on your language retention. Would you be able to have that time over the summer on top of doing things for your PS and preparing for admissions tests?

Have you considered Oxford? They let you take two AHs and an extra higher.