Transcripts required for application, but my school doesn't really have any I'm currently in the job market for tenure-track applications in mathematics. I have seen that some of the positions ask for undergraduate or graduate transcripts (both unofficial and official). 

I have an issue, especially with graduate transcripts: I obtained my Ph.D. in France, and I didn't had any coursework or anything, only my thesis. Thus there are no transcripts per se, only a certificate that I completed all the requirements. Would such a thing be enough for positions asking for transcripts?
The request for transcripts makes sense for students from PhD programs in the US, since the PhD program typically includes a substantial amount of course work. In your case, all that you can provide is documentation that you completed the PhD.  I've seen many applications like this.  That should be sufficient to get your application to the search committee although the committee may be uncomfortable with your lack of graduate level courses.    

For positions in which teaching is important, and the candidate will be expected to teach a variety of courses, it is reasonable for the search committee to look for evidence that a candidate has a broad enough background to teach a variety of courses as well as a willingness to do so.  

You might be surprised by the breadth that is necessary.  For example, although my PhD dissertation was in optimization, I've taught lower division courses in calculus, discrete mathematics for computer science, linear algebra, and differential equations, plus upper division and graduate level courses in linear and nonlinear programming, combinatorial optimization, numerical analysis, numerical linear algebra, mathematical modeling, vector calculus, probability and statistics, stochastic processes, time series analysis, and discrete event simulation.  I acquired much of the background for this by taking courses in my PhD program and preparing for and taking preliminary exams in several areas of mathematics.

In my experience interviewing candidates for faculty positions, I've often been disappointed by candidates with non-US PhD's who were too narrow in their background and teaching interests.    

Although you don't have a transcript of courses from your PhD, it would be in your interest to provide a transcript of courses that you took in your undergraduate and master's studies to provide some indication of your breadth.   You should also make a point in your teaching statement of explaining what you would like to teach, what you could teach even if it isn't your favorite area, and what you wouldn't feel properly prepared to teach.   This is also a question that is likely to come up during interviews.