I'm asking more specifically about the French intervention phase from 1635-1648. In my research, I'm seeing a lot of information on Scottish involvement, but I'm more interested in how the Irish were involved. I realize, however, that many were probably extremely occupied with the Three Kingdoms Wars, famine, and various rebellions at the time. So, I understand that they may not have been involved at all. I did find a work called "Irish Participation in Scandianavian Armies during the Thirty Years' War" but have no access to the document and, accounting for the spelling error, am unsure of the piece's validity regardless.
The Thirty Years' War was such a huge conflict, and such a magnet for mercenaries from all over Europe, that it would be surprising if no Irishmen were involved in it, and the beginnings of the British civil wars – which certainly began to stir with rebellion in Ireland late in 1641 – came relatively late in the European conflict. However, the evidence seems to suggest that the numbers were fairly small, certainly when compared to the very large numbers of Scots who participated.
According to Steve Murdoch of the University of Aberdeen,
Irishmen served as mercenaries in northern armies [from the 1620s]. The acts of the Privy Council refer to a levy of 2,000 Irish soldiers for Polish service, on condition that they were not used against the Protestant powers of Sweden, Denmark-Norway or Brandenburg. A reliable Swedish source, the agent Anders Svensson, casts doubt on the numbers of Irishmen actually raised, referring to an integrated contingent from all three Stuart kingdoms. On 30 August 1621, Svensson wrote to the Swedish king to announce the arrival of the Polish envoy in the Danish Sound with 300 Irish soldiers bound for Riga. He added that they were the advance guard of a total of 1,400 troops, with 800 more from England and Ireland and 300 from Scotland to follow.
More Irish were recruited for Swedish service in 1623 under the direction of the Scot, Colonel Robert Stewart who used an Irish captain by the name of Butler to recruit soldiers in Ireland. Certainly some of Stewart’s troops got through, though the Danish king did place obstacles in the way of free passage. In 1637, Colonel Stuart, another Scotsman, received permission to levy in Ireland for Swedish service. However some of the Irish recruits deserted in Scotland where they were accused of ‘lurking in obscure places’. The commission to arrest deserters granted by the Scottish Privy Council shows that the regiment included a mix of Ulster-Scots, Old English and Gaelic Irish.
By way of comparison, the number of Scottish officers fighting for the Danish king alone during the Thirty Years' War was enormous. Averaging out figures for the period 1618-48, Murdoch calculates that no less than 90 percent of Danish officers participating in the war were of Scottish origin.
Source
Steve Murdoch, 'Northern Exposure: Irishmen and Scandinavia in the seventeenth century,' in Early Modern History (1500-1700), 3 (1998)