(1) budget. Food at target rate of €300 a month sounds high for one person. We spend less than that for two of us in the UK. So sounds like you could still do better there, buying more in bulk and learning to cook a handful of economical good meals at home maybe? Though perhaps as your rent is low in a shared place you have limited access to a good kitchen, so rent may offset this for the moment.
Only point I'd make is that you don't list any consideration/allowance for irregular expenses like a holiday cost, flights to visit family etc. As Dublin to Paris etc. could be €100 return two or three times a year if you don't go on major holidays elsewhere then it's only €30 a month average so a small error. But if you do take/plan to take major holidays that could eat up a month or two of planned savings.
(2) Immediate savings. As you're just starting a simple savings account sounds like a good plan, you then have more time to think about other options.
(3) I don't know specifically about the Irish market but what we have in the UK is online investment platforms (see
http://monevator.com/compare-uk-cheapest-online-brokers/ for a list), these allow you to invest in various funds including all the main Vanguard ones. Typically they charge a 0.25% platform fee, which is only £25 a year on £10,000 invested, so would suit you well to access the low-cost Vanguard funds etc. The platforms normally only have a £100 minimum investment etc. and allow monthly investments at low costs (they'll batch up your purchase with others to keep costs down). You're right about the £100k minimum to work directly with Vanguard, but no such minimum for the fund platforms. There must be similar fund platforms in Ireland, or perhaps some of the UK ones operate in Ireland as well.
In terms of investments, it's of course up to you. Personally I prefer passive investments / index trackers and look to minimize fees, so use Interactive Investor for a £20 quarterly fee (is cheaper to pay that than a 0.25% fee as I've a fair amount invested), and two Vanguard funds at 0.15% and 0.25% OCF (annual charge). When you're just starting off and may need the money back in the short/medium term (towards buying a house and other life changes) then you might prefer lower risk funds like bond tracker funds rather than equities. The Vanguard LifeStrategy funds are a possible middle ground as they offer a mix of equity and bonds all under one fund.
Ultimately those are all investments that you can easily sell so you're not tied into the Irish economic system, and you don't have to invest in Irish funds or equities.
(4) Irish pension. Again I don't know the Irish market. However the UK pension legislation currently requires that you are allowed to transfer a contribution-based pension (i.e. cash contributions and investments) from the UK to another qualifying pension in the EU. So I'd therefore assume that's an EU directive so also applies to Ireland, so if you create a pension in Ireland you should be able to take it with you e.g. if you move back to France later on.
The advantages of a pension are the up front tax-relief, so you would get €100 in your pension for every €80 of take home pay given up as a 20% tax payer. €20 in €80 is equivalent to an instant 25% profit, so isn't bad. However, if your salary increases in a few years and you become a 40% tax payer then the tax savings on those earnings would be even higher, assuming Ireland gives the full tax relief as the UK does. So on the other hand you might decide a pension isn't a priority until you're paying a higher rate of tax.
The other advantage of a pension is that the investments grow tax-free afterwards (in the UK the exception is that there is some tax retained on dividends, but it's a small difference overall).
So really it is worth having a pension due to the tax savings, and provided Ireland has the rules on pensions transfers, there would be no reason for you not to set one up. In terms of how much to contribute, it's a decision. The UK applies a contribution limit of £40k a year, if you can afford to then in terms of optimizing your long-term wealth, then you would contribute as much as possible. But of course the money is tied up for a long time (55 in the UK though state pension age is 68). So you have to decide. In the UK the default rules ("auto enrolment" pension) are 5% of your gross salary plus a 3% employer contribution. Sounds like in Ireland the employer isn't forced to contribute, but as a starting point putting in 5% to 10% of your gross salary would be in line with the UK position.
Most of the UK fund platforms I mentioned above allow you to create a pension as well. That pension has nothing to do with your employer and you don't need their consent/to tell them, at least in the UK. You then have access to all the same funds again for investment within the pension.
Other thing to mention: in the UK we have ISAs (individual savings accounts), US equivalent is Roth IRA I believe (though there are some differences), these accounts allow you to put in savings after paying normal income tax, such that the savings interest paid or investment gains/dividends are tax free. The UK ISA limit was recently changed to around £15k a year, so if Ireland has anything similar you could put all of your monthly savings under that shelter to avoid interest/investment gain tax on their returns. These are flexible because you can always take the money out again (Roth IRA applies a tax charge I believe whereas ISAs don't).
(5) Overall. I'd say you're in a great position because at 21 you're already thinking seriously about these things. Most people, if they do it at all, only think properly about these things much later, when they will have potentially wasted thousands on excessive spending or not optimized their taxes/investments from the start.
While at 21 I wasn't specifically aware of concepts like FIRE and early retirement, I have been a saver since childhood (mental image of the 6-year old boy saving up his pocket money to put in his child savings account at the post office...) so have managed to do similar things overall. From my experience I do think I missed out on one obvious trick, which was that after the high savings interest rates came down after the 2008 recession, it took me several years to realize that having nearly all of my savings in cash in the period of 2009 to 2015 resulted in me missing out in a lot of investment growth (compared to a low risk bonds fund even), so while you don't need to jump into investments straight away, I would remind you to consider that if you hold cash savings rather than some form of investments, over the medium and long term you will miss out on a lot of growth, so do plan to choose to invest savings rather than holding too much cash.
Other consideration is that while tax-free investment growth in ISAs/pensions etc. may not seem relevant to you at the moment (e.g. if your investment growth is below the tax threshold), if you put money in these accounts up front, you will set yourself up better for the future when you would expect to earn more and hence pay more tax and have larger investment/savings returns. I didn't use all of my ISA allowances while a student, even though I had cash savings available, because at the time I wasn't paying tax anyway and didn't consider the implications for the future.
