What are my rights if I fell on a wet floor at a fast food restaurant and there were no signs or carpet?

Legally, if the restaurant was negligent, or careless, in not putting out signs about a wet floor or not mopping up the water--which they may have been; it's difficult to tell without more details, since it depends on why there was liquid on the floor, if the restaurant staff knew or reasonably should have known there was liquid, and if they had the time or chance to do something abou it--and their failure to do so led to the accident, they would be liable to any injuries, regardless of whether there is a broken bone or not.

Practically, it is very unlikely that it would be taking legal action for a level 2 sprain. That is because in a lawsuit, you recover compensation equivalent to your costs, losses, and, for injuries which cause weeks or more of significant life impairment, some amount of "pain and suffering." In a case like this, you could recover your out-of-pocket (not paid by insurance) medical costs; lost wages, if you missed any work; other out of pocket costs (such as is if you had to pay to take cabs to work instead of a bus or train, while your ankle heals); and possibly a *small* amount for pain and suffering (unless your ankle never heals right and you have permanent disabilty; then might get at least a modest amount for pain and suffering, but still very little compared to, say, loss of a limb or impairment of vision). However, to get that, if the restaurant (or its insurer) does not voluntarily pay you, you'd have to sue them; and for a personal injury lawsuit, you'd need to have a medical expert witness testify, and such witnesses commonly cost $1000 - $3000 or more for their time spent examining you, filling out reports, testifing, etc. You could spend as much or more on the case then you would get back. 

This doesn't mean you can't ask the restaurant for compensation and tell them you may sue if you don't receive something--and maybe they will offer to pay some amount. But if they won't pay voluntarily, think hard about whether it would be worthwhile to actually sue.

Legally, if the restaurant was negligent, or careless, in not putting out signs about a wet floor or not mopping up the water--which they may have been; it's difficult to tell without more details, since it depends on why there was liquid on the floor, if the restaurant staff knew or reasonably should have known there was liquid, and if they had the time or chance to do something abou it--and their failure to do so led to the accident, they would be liable to any injuries, regardless of whether there is a broken bone or not.

Practically, it is very unlikely that it would be taking legal action for a level 2 sprain. That is because in a lawsuit, you recover compensation equivalent to your costs, losses, and, for injuries which cause weeks or more of significant life impairment, some amount of "pain and suffering." In a case like this, you could recover your out-of-pocket (not paid by insurance) medical costs; lost wages, if you missed any work; other out of pocket costs (such as is if you had to pay to take cabs to work instead of a bus or train, while your ankle heals); and possibly a *small* amount for pain and suffering (unless your ankle never heals right and you have permanent disabilty; then might get at least a modest amount for pain and suffering, but still very little compared to, say, loss of a limb or impairment of vision). However, to get that, if the restaurant (or its insurer) does not voluntarily pay you, you'd have to sue them; and for a personal injury lawsuit, you'd need to have a medical expert witness testify, and such witnesses commonly cost $1000 - $3000 or more for their time spent examining you, filling out reports, testifing, etc. You could spend as much or more on the case then you would get back. 

This doesn't mean you can't ask the restaurant for compensation and tell them you may sue if you don't receive something--and maybe they will offer to pay some amount. But if they won't pay voluntarily, think hard about whether it would be worthwhile to actually sue.