Grammatically, it's fine to start a sentence with "Because" in a construction like this one: "Because...codes" here is a subordinate clause (that is, it couldn't stand on its own as a sentence) that introduces the main part of the sentence (everything after the comma). When teachers warn us against starting sentences with "Because," it's to prevent us from winding up with sentence fragments, which can easily result from punctuating in the wrong place.
For example, suppose I write the following:
"I plan to go shopping for office clothes this weekend. Because I'll be starting a new job on Monday."
That's not grammatical. The second "sentence" here--"Because I'll be starting a new job on Monday"--isn't a complete sentence. It can't stand alone and make sense.
But either of the following are quite correct sentences, because each could stand alone and still make sense:
"I plan to go shopping for office clothes this weekend, because I'll be starting a new job on Monday."
"Because I'll be starting a new job on Monday, I plan to go shopping for office clothes this weekend."
I do agree that in your draft sentence, the introductory bit is too long. It's not technically a run-on sentence, but it definitely takes a long time to get to the "real action." Readers could get a bit lost on the way. Here's one suggested rewrite:
"I would be proud to work for Fortuna because it maintains such high safety levels and adheres strictly to environmental codes."
If this is a job applicaiton, it's probably not necessary to remind the reader that the company's business is natural gas. And you can flatter the company without sounding like an ad for it, which is why I'd suggest dropping "ever vigilant business practices." If you do keep that phrase, make sure you use "its" (no apostrophe) to refer to the company: "it's" (with the apostrophe) means either "it is" ("It's a nice day") or "it has" ("It's been nice chatting with you").
Years of teaching business writing and editing, including several years in an employment agency helping people to write effective resumes and covering letters. For definition of "subordinate clause" (and several other examples), see http://englishplus.com/grammar/00000010.htm.