No, the pattern used among English native speakers is as you say:
If I [past tense], I would [infinitive]
Because of native language influence on second language speakers, you may sometimes see "would" in both parts of the sentence, but it's not native usage.
N.B. This doesn't mean that "if I" is never followed by "would" ever ever in English (there seems to be some confusion about this given the corpus examples cited by @kiamlaluno), just that it generally isn't in this particular pattern with the intended meaning. Clearly you can construct other grammatical sentences of English, involving different structures/uses of "would", which do contain the sequence "if I would". ("Every time he asked if I would be able to help, I had to decline.")
(On a theoretical note, I am one of those that would avoid the idea of calling the past tense a "subjunctive" here: it's far from clear that English has a subjunctive paradigm.)