Using eval_pv, you'd have to initialise the string as Perl code.

eval_pv("$string = \"This is a string\"; print(\"$string\\n\");");
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What you really want is call_*. Look at "Passing Parameters" in perlcall.

static void call_some_perl_sub(const char* s) {
    dSP;
    ENTER;
    SAVETMPS;
    PUSHMARK(SP);
    XPUSHs(sv_2mortal(newSVpv(s, strlen(s))));
    PUTBACK;
    call_pv("some_perl_sub", G_DISCARD);
    FREETMPS;
    LEAVE;
}
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Where some_perl_sub does your printing. eval_pv can be used to create the sub in the first place.

Update: Added code.