How wide spread is it? Do you know what percentage you have? as Rye grass is used in very hard wearing areas not usually for small lawns or it may be used as an economic lawn seed/turfs.
Normally grass seed is a mixture and if you have a mixture of lawn seeds then regular mowing every 5-7 days will improve the appearance and texture.
However, if you have a high percentage of Rye grass then a coarse lawn is how it is and and although mowing will improve it, it will never be a fine grassed lawn.

There isn't one - any weed treatments for grass, naturally enough, don't kill grasses. As Drc says, most lawns contain a percentage of rye grass because its hardwearing, although better mixes only use short leaved rye and not the tufty, longer stuff. If you want luxury turf, you'd need to replace the grass you have with fine leaved, luxury grade, but if you do, be aware it will not withstand relatively normal use, its more for looking at and needs high levels of maintenance.