I think it's got a chance actually - it's mainly searching for past life. It's the first mission to Mars with the ability to drill below the surface, able to drill 2 meters down. This is not really as deep as you'd hope, you'd like to be able to drill ten meters, but it's a good start. The aim is to find ancient clays  or salts with organics that were deposited by life. Most importantly you have to be able to distinguish this from organics from meteorites, and they think they can do that.

They are headed for an area of Mars Oxia Planum with many layers of clay, complex geology, and the clays were exposed only recently, but deposited over 3 billion years ago. It also has a large delta or aluvial fan. (see also Landing site recommended for ExoMars 2018 )

So - I think first decent chance of finding ancient life on Mars.

We have no idea what kind of life it would be, what habitats it preferred, how advanced it would be, what biology it would have. And it has to be buried quickly, not eaten, preserved for billions of years not washed away by floods, and then exposed quickly. Still, it's got a large area to search, varied and complex geology, many strata, and it may find life that has been preserved through all that.

It's not really searching for present day life, but does have the capability. And according to some ideas, there may be life even in the equatorial regions of Mars and not just in the "warm seasonal flows". If so then perhaps it will find it.

Some scientists think Viking already found life in the 1970s. See Rhythms From Martian Sands - What Did Our Viking Landers Find in 1976? Astonishingly, We Don't Know

We've never done any follow up experiments. Curiosity would not be able to confirm or deny this result, if true.

If so, ExoMars is the first rover since Viking to have a chance of confirming this, or at least getting additional suggestive data. It was able to detect life in the dry desert core of the Atacama desert, by its chirality, which is quite a challenge.

http://www.berkeley.edu/news/med...

I'm not sure it is sensitive enough to disprove this Viking result, since the controversial Viking labelled release was capable of detecting a tiny signal of a few cells which it then grew in a medium, at least that was the idea.

But it could potentially confirm it. If so there'd be a lot of interest in that.

There are also theoretical ideas that could permit life there, either using the 100% night time moisture, also Nilton Renno thinks that there is some possibility that life could use biofilms or something similar to exploit the new liquid layer foudn beneath the sand indirectly by Curiosity. The usual idea is that it is either warm enough for life, but too salty, or fresh enough for life, but too cold, and never both together. Nilton Renno thinks there might be a chance that using biofilms or other methods, life could modify this environment to make it habitable, if so there could be life just a cm or so below the sand Curiosity was driving over, and ExoMars would have a chance of finding it.

Present day life is likely to be sparse and hard to find in such extreme conditions - so you might need to sample in many places before you find it. Anyway this is not its priority; it would be sent to a different part of Mars if the aim was to find present day life. But it has a chance.

I think of the missions coming up in the near future, ExoMars has by far the best chance of finding past or present day life on Mars in 2018 or whenever it gets there.

The Trace Gas Orbiter has a chance of finding more about the methane also. Right now then I think the ESA with Russia is just about to get to the leading edge of Mars life exploration. At least it will if it can keep on track and they are doing everything right. If any of the landings fail, surely they will try again.