It probably wouldn't increase top speed. That's a matter of how much drag the car generates versus how much horsepower the engine produces. You figure out what speed that amount of horsepower can produce and gear it so at that speed the engine is at the revs it produces peak horsepower at. Either shortening or lengthening the gearing from there will produce a lower top speed. It appears the gearing for the 172 and 182 and 197 are all very very close to what produces maximum speed in top gear.
What you could do is change the gear ratios so that that 5th gear produces that ideal gearing. And 6th is an overdrive for quieter and more economical cruising.
The problem with that is that it would require either a taller diff ratio, which would mean all the gears would be taller, so moving away in 1st would be like trying to move off in 2nd is now, or it would require a more wide ratio set of gears, ie bigger gaps between the gears. As a manufacturer tunes an engine more that moves the peak power further up the rev range, but it doesn't widen the power band. So the engine needs a closer ratio gearbox to make sure it stays in the powerband. All these factors came together to mean that when Renault decided it was going to build a significantly bigger and therefore heavier new Clio Sport with a more highly tuned version of the same engine it could get pretty close to the same outright performance in both acceleration and top speed, but to do it it needed a closer ratio gearbox with more gears. If you try to change the gearbox ratios to widen them out you will actually get less performance not more.
What would solve your problem is one of a couple of things:
1. somehow reduce the weight back to 172/182 weight, that'd solve a lot of problems, but it would require losing stuff like air conditioning, or reducing safety, or high priced lightweight parts made out of expensive materials like carbon fibre, or
2. even more gears, eg, a 7 speed gearbox with 7th as an overdrive that you'd only use for cruising on the motorway, or
3. a CVT (continuously variable ratio) automatic transmission with a range of ratios from as low as the manual gearbox's first to something higher than the current 6th for motorway cruising, and these are available, but unfortunately they are less efficient than a manual gearbox, so less power would get from the engine to the wheels and the car would have a lower top speed, or
4. either a bigger capacity engine, or the equivalent of it, by which I mean one with a low boost turbo or supercharger, or an engine with something like Honda's intelligent VTEC system that allows more top end horsepower without losing bottom end torque. This would allow you to produce more torque and just as much power (or more) at lower revs meaning the close ratio gearbox wouldn't be required, and 6th could be lengthened to make it a motorway gear.
I'm sorry, but Renault's engineers aren't idiots. There are plenty of fixes, but if there was an obvious easy cheap one they would have done it, wouldn't they.
What you'll see in the next few years is car manufacturers going to slightly smaller engines, but fitted with low boost turbos, to achieve the same apparent feel to the driver as a bigger engine but with better fuel economy. So you'll buy a Laguna or a Mondeo, and instead of a 2.0, it'll have a low-boost turbo 1.6. And that engine will also fit in the next body-size down to make a performance model.
