How can I progress with researching/working with profs with a bad transcript? I've been asking a lot of questions on here lately (my apologies to the admin for that), but I've become very worried about my future as I've had a terrible semester. 

I'm a second year student currently studying mathematics at a Canadian university and as of now, I have two Cs (one in a math course) and an F on my transcript (thankfully, from a non math course). I'm very worried about how this will hurt my application to grad school (in terms of getting research experience and my transcript itself), particularly as a MSc candidate. I know I have a lot of time to make up for my mistakes (academically) this semester, but the way I see it, I'm pretty much out of options until maybe next year when my GPA (currently sitting at ~3.4-3.45) goes up, considering a lot of research opportunities at my school are based on GPA. 

I am very interested in pursuing research in some areas of pure mathematics. However, like I mentioned earlier, I know for a fact my school operates research grants and applications based on GPA and seniority, thus because I: 


Am a second year student and do not have many higher level maths courses under my belt and; 
Have a mediocre GPA and;
Have received lower marks for second year courses rather than first...


it is highly likely I will get rejected by the professors at my school and not get the grant. 

My question now is what else can I do to help me gain experience/skills/contacts within the department at my school? My lackluster grades were a result of poor time management and I know I can do better. When I asked a similar question, I was recommended to seek professors to do informal reading with. I am still planning on doing that, however, is there anything else that I can do? I was hoping to ask one of my profs, but I ended up doing much worse in his course than I expected, so I don't know if contacting him would be reasonable anymore? 

Anyway, this is a question mostly to see what I can do to redeem myself more than anything. I still have two more maths courses this coming semester I have the chance to do well in, and so far this C would be my lowest maths-related mark yet. Hopefully that doesn't completely take my out of the running. 

Thanks in advance for all your help.
Honestly, you should take a step back and focus on your coursework first. Research experience is great and often necessary for graduate applications, but it's useless if you don't have good grades in upper-level classes. Focus on showing that you can do well in courses before worrying about adding research to your workload.

Also, excelling in an upper-level class is the probably the best way to connect with a professor and get a research opportunity at this point. If you can get to know a professor a little through class and office hours and impress them there, then it's much easier to ask them after the class is over about research opportunities. The key, however, is that you have to actually impress them, and no professor is going to be impressed by a C or even a B in their class.

It also helps if you are willing to work as an unpaid research assistant or similar. Getting funded positions as an undergraduate can be very difficult, especially in math since it's unlikely you will do any real work. But unpaid positions can still be very valuable and are much easier to obtain.